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$3.75 in quarters and nickles in her car. The number of nickles is fifteen more than the number of q
$3.75 in quarters and nickels in her car. The number of nickels is fifteen more than the number of quarters. How many of each type of coin does she have? Let the number of nickels be n, and the number of quarters be q. We know nickels are 0.05, and quarters are 0.25. We're given: [LIST=1] [*]n = q + 15 [*]0.05n + 0.25q = 3.75 [/LIST] Substituting (1) into (2), we get: 0.05(q + 15) + 0.25q = 3.75 0.05q + 0.75 + 0.25q = 3.75 Combine like term: 0.3q + 0.75 = 3.75 [URL='https://www.mathcelebrity.com/1unk.php?num=0.3q%2B0.75%3D3.75&pl=Solve']Typing this equation into our calculator[/URL], we get: [B]q = 10[/B] Substituting q = 10 into Equation (1), we get: n = 10 + 15 [B]n = 25[/B]
(3,-4) lies on the line with equation 3x-2y=k, find k
(3,-4) lies on the line with equation 3x-2y=k, find k Plug in our values: 3(3) -2(-4) = k 9 + 8 = k k = [B]17[/B]
(3,3) radius of 4
(3,3) radius of 4 We have a circle with center (3,3) with a radius of 4. [URL='https://www.mathcelebrity.com/eqcircle.php?h=3&k=3&r=4&calc=1&d1=-1&d2=2&d3=3&d4=2&ceq=%28x+%2B+3%29%5E2+%2B+%28y+-+2%29%5E2+%3D+16&pl=Calculate']Use our circle equation calculator to get the general form and standard form.[/URL]
-28 is the solution to the sum of a number p and 21
-28 is the solution to the sum of a number p and 21 The sum of a number p and 21: p + 21 The phrase [I]is the solution to[/I] means an equation, so we set p + 21 equal to -28: [B]p + 21 = -28 [/B] If the problem asks you to solve for p, then we [URL='https://www.mathcelebrity.com/1unk.php?num=p%2B21%3D-28&pl=Solve']type this into our search engine[/URL] and we get: p = [B]-49[/B]
-65 times the difference between a number and 79 is equal to the number plus 98
-65 times the difference between a number and 79 is equal to the number plus 98 The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. The first expression, [I]the difference between a number and 79[/I] means we subtract 79 from our arbitrary variable of x: x - 79 Next, -65 times the difference between a number and 79 means we multiply our result above by -65: -65(x - 79) The phrase [I]the number[/I] refers to the arbitrary variable x earlier. The number plus 98 means we add 98 to x: x + 98 Now, let's bring it all together. The phrase [I]is equal to[/I] means an equation. So we set -65(x - 79) equal to x + [B]98: -65(x - 79) = x + 98[/B] <-- This is our algebraic expression If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=-65%28x-79%29%3Dx%2B98&pl=Solve']type this equation into our search engine[/URL], and you get: x = [B]76.31818[/B]
1 integer is 7 times another. If the product of the 2 integers is 448, then find the integers.
1 integer is 7 times another. If the product of the 2 integers is 448, then find the integers. Let the first integer be x and the second integer be y. We have the following two equations: [LIST=1] [*]x = 7y [*]xy = 448 [/LIST] Substitute (1) into (2), we have: (7y)y = 448 7y^2 = 448 Divide each side by 7 y^2 = 64 y = -8, 8 We use 8, since 8*7 = 56, and 56*8 =448. So the answer is [B](x, y) = (8, 56)[/B]
1 year from now Mike will be 40 years old. The current sum of the ages of Mike and John is 89. How o
1 year from now Mike will be 40 years old. The current sum of the ages of Mike and John is 89. How old is John right now? If Mike will be 40 1 year from now, then he is: 40 - 1 = 39 years old today. And if the current sum of Mike and John's age is 89, then we use j for John's age: j + 39 = 89 [URL='https://www.mathcelebrity.com/1unk.php?num=j%2B39%3D89&pl=Solve']Type this equation into our search engine[/URL], and we get: [B]j = 50[/B]
1 year from now Paul will be 49 years old. The current sum of the ages of Paul and Sharon is 85. How
1 year from now Paul will be 49 years old. The current sum of the ages of Paul and Sharon is 85. How old is Sharon right now? If Paul will be 49 years old 1 year from now, this means today, he is 49 - 1 = 48 years old. Let Sharon's age be s. Then from the current sum of Paul and Sharon's ages, we get: s + 49 = 85 [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B49%3D85&pl=Solve']Type this equation into our search engine[/URL], and get: s = [B]36[/B]
1/2a-10b=c solve for a
1/2a-10b=c solve for a Multiply each side of the equation by 2: 2/2a - 2(10)b = 2c Simplify: a - 20b = 2c Add 20b to each side: a - 20b + 20b = 2c + 20b Cancel the 20b on the left side: [B]a = 2c + 20b [/B] You can also factor out a 2 on the left side for another version of this answer: [B]a = 2(c + 10b)[/B]
1/4 of the difference of 6 and a number is 200
1/4 of the difference of 6 and a number is 200 Take this [B]algebraic expression[/B] in 4 parts: [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x [*]The difference of 6 and a number means we subtract x from 6: 6 - x [*]1/4 of the difference means we divide 6 - x by 4: (6 - x)/4 [*]Finally, the phrase [I]is[/I] means an equation, so we set (6 - x)/4 equal to 200 [/LIST] [B](6 - x)/4 = 200[/B]
1/a + 1/b = 1/2 for a
1/a + 1/b = 1/2 for a Subtract 1/b from each side to solve this literal equation: 1/a + 1/b - 1/b = 1/2 - 1/b Cancel the 1/b on the left side, we get: 1/a = 1/2 - 1/b Rewrite the right side, using 2b as a common denominator: 1/a = (b - 2)/2b Cross multiply: a(b - 2) = 2b Divide each side by (b - 2) a = [B]2b/(b - 2)[/B]
10 is twice the sum of x and 5
10 is twice the sum of x and 5 The sum of x and 5 means we add: x + 5 Twice the sum means we multiply by 2: 2(x + 5) The word [I]is[/I] means an equation, so we set 2(x + 5) equal to 10 [B]2(x + 5) = 10[/B]
10 times a number is 420
10 times a number is 420 A number denotes an arbitrary variable, let's call it x. 10 times a number: 10x The phrase is means equal to, so we set 10x equal to 420 [B]10x = 420 <-- This is our algebraic expression [/B] If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=10x%3D420&pl=Solve']equation calculator[/URL] We get x = 42
10 times the first of 2 consecutive even integers is 8 times the second. Find the integers
10 times the first of 2 consecutive even integers is 8 times the second. Find the integers. Let the first integer be x. Let the second integer be y. We're given: [LIST=1] [*]10x = 8y [*]We also know a consecutive even integer means we add 2 to x to get y. y = x + 2 [/LIST] Substitute (1) into (2): 10x = 8(x + 2) Multiply through: 10x = 8x + 16 To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=10x%3D8x%2B16&pl=Solve']we type this equation into our search engine[/URL] and we get: [B]x = 8[/B] Since y = x + 2, we plug in x = 8 to get: y = 8 + 2 [B]y = 10 [/B] Now, let's check our work. Does x = 8 and y = 10 make equation 1 hold? 10(8) ? 8(10) 80 = 80 <-- Yes!
104 subtracted from the quantity 6 times r is the same as r
104 subtracted from the quantity 6 times r is the same as r The quantity 6 times r means we multiply 6 by r: 6r 104 subtracted from 6r is written as: 6r - 104 [B]The phrase [I]is the same as[/I] means we have an equation. So we set 6r - 104 equal to r 6r - 104 = r[/B]
10ac-x/11=3 for a
10ac-x/11=3 for a Add x/11 to each side of the equation to isolate a: 10ac - x/11 + x/11 = 3 + x/11 Cancelling the x/11 on the left side, we get: 10ac = 3 + x/11 Divide each side by 10c to isolate a: 10ac/10c = 3 + x/11 Cancelling the 10c on the left side, we get: a = [B]3/10c + x/110c[/B]
12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37
12 is multiplied by some number, that product is reduced by 9, and the total is equal to 37 The phrase [I]some number[/I] means an arbitrary variable, let's call it x. 12 multiplied by this number: 12x The product of 12x is reduced by 9 12x - 9 The phrase [I]the total is equal to[/I] means an equation, so we set 12x - 9 equal to 37: [B]12x - 9 = 37[/B]
12 plus 6 times a number is 9 times the number
12 plus 6 times a number is 9 times the number The phrase [I]a number [/I]means an arbitrary variable. Let's call it x. 6 times a number is written as: 6x 12 plus 6 times the number means we add 6x to 12: 12 + 6x 9 times a number is written as: 9x The phrase [I]is[/I] means an equation, so we set 12 + 6x equal to 9x [B]12 + 6x = 9x <-- This is our algebraic expression[/B] [B][/B] If the problem asks you to solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B6x%3D9x&pl=Solve']type this expression into our search engine[/URL] and you get: x = [B]4[/B]
1225 people live in a village,329 are men and 404 are women. how many are children
1225 people live in a village,329 are men and 404 are women. how many are children We can have either men, women, or children. We have the following equation where children are "c". 239 + 404 + c = 1225 To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=239%2B404%2Bc%3D1225&pl=Solve']type this equation into our search engine[/URL] and we get: c = [B]582[/B]
132 is 393 multiplied by y
132 is 393 multiplied by y 393 multiplied by y 393y The word [I]is[/I] means equal to, so we set 393y equal to 132 as our algebraic expression [B]393y = 132 [/B] If you need to solve for y, use our [URL='http://www.mathcelebrity.com/1unk.php?num=393y%3D132&pl=Solve']equation calculator[/URL]
15 added to the quotient of 8 and a number is 7.
15 added to the quotient of 8 and a number is 7. Take this algebraic expression in pieces: [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. [*]The quotient of 8 and a number: 8/x [*]15 added to this quotient: 8/x + 15 [*]The word [I]is[/I] means an equation, so we set 8/x + 15 equal to 7 [/LIST] [B]8/x + 15 = 7[/B]
15 cats, 10 have stripes, 7 have stripes and green eyes, how many cats have just green eyes
Let G be green eyes and S be Stripes, and SG be Stripes and Green Eyes. [U]Set up an equation[/U] Total Cats = Green Eyes + Stripes - Green Eyes and Stripes 15 = G + 10 - 7 15 = G + 3 [U]Subtract 3 from each side:[/U] [B]G = 12[/B]
17 decreased by three times d equals c
17 decreased by three times d equals c three times d means we multiply d by 3: 3d 17 decreased by three times d means we subtract 3d from 17 17 - 3d The word [I]equals[/I] means an equation, so we set 17 - 3d equal to c: [B]17 - 3d = c[/B]
175 students separated into n classes is 25
175 students separated into n classes is 25 175/n = 25 Cross multiply: 25n = 175 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=25n%3D175&pl=Solve']equation calculator[/URL], we get: [B]n = 7[/B]
2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than
2 baseball players hit 60 home runs combined last season. The first player hit 3 more home runs than twice a number of home runs the second player hit. how many home runs did each player hit? Declare variables: Let the first players home runs be a Let the second players home runs be b We're given two equations: [LIST=1] [*]a = 2b + 3 [*]a + b = 60 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for a: 2b + 3 + b = 60 Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B3%2Bb%3D60&pl=Solve']type this equation[/URL] in and get: b = [B]19 [/B] To solve for a, we substitute b = 19 into equation (1): a = 2(19) + 3 a = 38 + 3 a = [B]41[/B]
2 consecutive even integers that equal 118
Let x be the first even integer. That means the next consecutive even integer must be x + 2. Set up our equation: x + (x + 2) = 118 Group x terms 2x + 2 = 118 Subtract 2 from each side 2x = 116 Divide each side by 2 x = 58 Which means the next consecutive even integer is 58 + 2 = 60 So our two consecutive even integers are [B]58, 60[/B] Check our work: 58 + 60 = 118
2 consecutive odd integers such that their product is 15 more than 3 times their sum
2 consecutive odd integers such that their product is 15 more than 3 times their sum. Let the first integer be n. The next odd, consecutive integer is n + 2. We are given the product is 15 more than 3 times their sum: n(n + 2) = 3(n + n + 2) + 15 Simplify each side: n^2 + 2n = 6n + 6 + 15 n^2 + 2n = 6n + 21 Subtract 6n from each side: n^2 - 4n - 21 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-4n-21%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get: n = (-3, 7) If we use -3, then the next consecutive odd integer is -3 + 2 = -1. So we have [B](-3, -1)[/B] If we use 7, then the next consecutive odd integer is 7 + 2 = 9. So we have [B](7, 9)[/B]
2 Lines Intersection
Enter any 2 line equations, and the calculator will determine the following:
* Are the lines parallel?
* Are the lines perpendicular
* Do the lines intersect at some point, and if so, which point?
* Is the system of equations dependent, independent, or inconsistent
2 movie tickets and 3 snacks are $24. 3 movie tickets and 4 snacks are $35. How much is a movie tick
2 movie tickets and 3 snacks are $24. 3 movie tickets and 4 snacks are $35. How much is a movie ticket and how much is a snack? Let a movie ticket cost be m, and a snack cost be s. We have: 2m + 3s = 24.3 3m + 4s = 35 Using the [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=2m+%2B+3s+%3D+24.3&term2=3m+%2B+4s+%3D+35&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: m = $7.8 s = $2.9
2 numbers add to 200. The first is 20 less than the second.
2 numbers add to 200. The first is 20 less than the second. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x + y = 200 [*]x = y - 20 [/LIST] Plug (2) into (1) (y - 20) + y = 200 Group like terms: 2y - 20 = 200 [URL='https://www.mathcelebrity.com/1unk.php?num=2y-20%3D200&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]y = 110[/B] <-- This is the larger number Plug y = 110 into Equation (2) to get the smaller number: x = 110 - 20 [B]x = 90[/B] <-- This is the smaller number Let's check our work for Equation (1) using x = 90, and y = 110 90 + 110 ? 200 200 = 200 <-- Good, our solutions check out for equation (1) Let's check our work for Equation (2) using x = 90, and y = 110 90 = 110 - 20 90 = 90 <-- Good, our solutions check out for equation (2)
2 numbers that add up makes 5 but multiplied makes -36
2 numbers that add up makes 5 but multiplied makes -36 Let the first number be x and the second number be y. We're given two equations: [LIST=1] [*]x + y = 5 [*]xy = -36 [/LIST] Rearrange equation (1) by subtracting y from each side: [LIST=1] [*]x = 5 - y [*]xy = -36 [/LIST] Substitute equation (1) for x into equation (2): (5 - y)y = -36 5y - y^2 = -36 Add 36 to each side: -y^2 + 5y + 36 = 0 We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=-y%5E2%2B5y%2B36%3D0&pl=Solve+Quadratic+Equation&hintnum=0']type it in our search engine and solve[/URL] to get: y = ([B]-4, 9[/B]) We check our work for each equation: [LIST=1] [*]-4 + 9 = -5 [*]-4(9) = -36 [/LIST] They both check out
2 numbers that are equal have a sum of 60
2 numbers that are equal have a sum of 60 Let's choose 2 arbitrary variables for the 2 numbers x, y Were given 2 equations: [LIST=1] [*]x = y <-- Because we have the phrase [I]that are equal[/I] [*]x + y = 60 [/LIST] Because x = y in equation (1), we can substitute equation (1) into equation (2) for x: y + y = 60 Add like terms to get: 2y = 60 Divide each side by 2: 2y/2 = 60/2 Cancel the 2's and we get: y = [B]30 [/B] Since x = y, x = y = 30 x = [B]30[/B]
2 pens and 1 eraser cost $35 and 3 pens and 4 erasers cost $65. X represents the cost of 1 pen and Y
2 pens and 1 eraser cost $35 and 3 pens and 4 erasers cost $65. X represents the cost of 1 pen and Y represents the cost of 1 eraser. Write the 2 simultaneous equations and solve. Set up our 2 equations where cost = price * quantity: [LIST=1] [*]2x + y = 35 [*]3x + 4y = 65 [/LIST] We can solve this one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+%2B+y+%3D+35&term2=3x+%2B+4y+%3D+65&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]x (cost of 1 pen) = 15[/B] [*][B]y (cost of 1 eraser) = 5[/B] [/LIST]
2 times a number added to another number is 25. 3 times the first number minus the other number is 2
2 times a number added to another number is 25. 3 times the first number minus the other number is 20. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]2x + y = 25 [*]3x - y = 20 [/LIST] Since we have matching opposite coefficients for y (1 and -1), we can add both equations together and eliminate a variable. (2 + 3)x + (1 - 1)y = 25 + 20 Simplifying, we get: 5x = 45 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D45&pl=Solve']Typing this equation into the search engine[/URL], we get: [B]x = 9[/B] To find y, we plug in x = 9 into equation (1) or (2). Let's choose equation (1): 2(9) + y = 25 y + 18 = 25 [URL='https://www.mathcelebrity.com/1unk.php?num=y%2B18%3D25&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]y = 7[/B] So we have (x, y) = (9, 7) Let's check our work for equation (2) to make sure this system works: 3(9) - 7 ? 20 27 - 7 ? 20 20 = 20 <-- Good, we match!
2 times a number equals that number plus 5
2 times a number equals that number plus 5 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 2 times a number means we multiply 2 by x: 2x That number plus 5 means we add 5 to the number x x + 5 The phrase [I]equals[/I] means we set both expressions equal to each other [B]2x = x + 5[/B] <-- This is our algebraic expression If you want to take this further and solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3Dx%2B5&pl=Solve']type this expression in the search engine[/URL] and we get: [B]x = 5[/B]
2 times a number minus 4 times another number is 6. The sum of 2 numbers is 8. Find the 2 numbers
2 times a number minus 4 times another number is 6. The sum of 2 numbers is 8. Find the 2 numbers. Let the first number be x, and the second number be y. We're given two equations: [LIST=1] [*]2x - 4y = 6 [*]x + y = 8 [/LIST] Using our simultaneous equation calculator, there are 3 ways to solve this: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Substitution']Substitution[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Elimination']Elimination[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+4y+%3D+6&term2=x+%2B+y+%3D+8&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] They all give the same answers: (x, y) = [B](6.3333333, 1.6666667)[/B]
2 times as many dimes as quarters and they have a combined value of 180 cents, how many of each coin
2 times as many dimes as quarters and they have a combined value of 180 cents, how many of each coin does he have? Let d be the number of dimes. Let q be the number of quarters. We're given two equations: [LIST=1] [*]d = 2q [*]0.1d + 0.25q = 180 [/LIST] Substitute (1) into (2): 0.1(2q) + 0.25q = 180 0.2q + 0.25q = 180 [URL='https://www.mathcelebrity.com/1unk.php?num=0.2q%2B0.25q%3D180&pl=Solve']Typing this equation into the search engine[/URL], we get: [B]q = 400[/B] Now substitute q = 400 into equation 1: d = 2(400) [B]d = 800[/B]
2 times the quantity x minus 1 is 12
2 times the quantity x minus 1 is 12 The quantity x minus 1 is written as: x - 1 2 times this quantity: 2(x - 1) The word [I]is[/I] means an equation, so we set 2(x - 1) equal to 12: [B]2(x - 1) = 12[/B]
2 times the sum of a number and 3 is equal to 3x plus 4
2 times the sum of a number and 3 is equal to 3x plus 4 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The sum of a number and 3 means we add 3 to x: x + 3 2 times this sum means we multiply the quantity x + 3 by 2 2(x + 3) 3x plus 4 means 3x + 4 since the word plus means we use a (+) sign 3x + 4 The phrase [I]is equal to[/I] means an equation, where we set 2(x + 3) equal to 3x + 4 [B]2(x + 3) = 3x + 4[/B]
20 percent of my class is boys. There are 30 boys in class. How many girls in my class
20 percent of my class is boys. There are 30 boys in class. How many girls in my class? Let c be the number of people in class. Since 20% = 0.2, We're given: 0.2c = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=0.2c%3D30&pl=Solve']Type this equation into our search engine[/URL], we get: c = 150 Since the class is made up of boys and girls, we find the number of girls in the class by this equation: Girls = 150 - 30 Girls = [B]120[/B]
20% of a number is x. What is 100% of the number? Assume x>0.
20% of a number is x. What is 100% of the number? Assume x>0. Let the number be n. We're given: 0.2n = x <-- Since 20% = 0.2 To find n, we multiply each side of the equation by 5: 5(0.2)n = 5x n = [B]5x[/B]
217 times u, reduced by 180 is the same as q
217 times u, reduced by 180 is the same as q. Take this algebraic expression pieces: Step 1: 217 times u We multiply the variable u by 217 217u Step 2: reduced by 180 Subtract 180 from 217u 217u - 180 The phrase [I]is the same as[/I] means an equation, so we set 217u - 180 equal to q [B]217u - 180 = q[/B]
223 subtracted from the quantity 350 times a is equal to b
223 subtracted from the quantity 350 times a is equal to b Take this algebraic expression in parts: [LIST] [*]the quantity 350 times a: 350a [*]223 subtracted from the quantity: 350a - 223 [*]The phrase [I]is equal to[/I] means an equation, so we set 350a - 223 equal to b [/LIST] [B]350a - 223 = b[/B]
23 decreased by thrice of y is not equal to 15
Thrice of y means multiply y by 3 3y 23 decreased by 3y means we subtract 23 - 3y Is not equal to means we set up an equation with not equal sign 23 - 3y <> 15
231 is 248 subtracted from the quantity h times 128
231 is 248 subtracted from the quantity h times 128 Let's take this algebraic expression in parts: [LIST=1] [*]h times 128: 128h [*]24 subtracted from this: 128h - 248 [*]The word [I]is[/I] means an equation, so we set 128h - 248 equal to 231 [/LIST] [B]128h - 248 = 231[/B] <-- This is our algebraic expression If the problem asks you to solve for h, then you [URL='https://www.mathcelebrity.com/1unk.php?num=128h-248%3D231&pl=Solve']type in this equation into our search engine[/URL] and get: h = [B]3.742[/B]
249 equals 191 times c, decreased by 199
249 equals 191 times c, decreased by 199 [U]Take this in pieces:[/U] 191 times c: 191c The phrase [I]decreased by[/I] means we subtract 199 from 191c: 191c - 199 We set this expression equal to 249: [B]191c - 199 = 249[/B] <-- This is our algebraic expression If you want to solve for c, type this equation into the search engine and we get: [B]c = 2.346[/B]
298 is the same as c and 230 more
[I]Is the same as[/I] means equal to. 230 more means we add 230. Set up this equation: c + 230 = 298 To solve for c if needed, visit our [URL='http://www.mathcelebrity.com/1unk.php?num=c%2B230%3D298&pl=Solve']calculator[/URL]. c = 68
2consecutiveevenintegerssuchthatthesmalleraddedto5timesthelargergivesasumof70
2 consecutive even integers such that the smaller added to 5 times the larger gives a sum of 70. Let the first, smaller integer be x. And the second larger integer be y. Since they are both even, we have: [LIST=1] [*]x = y - 2 <-- Since they're consecutive even integers [*]x + 5y = 70 <-- Smaller added to 5 times the larger gives a sum of 70 [/LIST] Substitute (1) into (2): (y - 2) + 5y = 70 Group like terms: (1 + 5)y - 2 = 70 6y - 2 = 70 [URL='https://www.mathcelebrity.com/1unk.php?num=6y-2%3D70&pl=Solve']Typing 6y - 2 = 70 into our search engine[/URL], we get: [B]y = 12 <-- Larger integer[/B] Plugging this into Equation (1) we get: x = 12 - 2 [B]x = 10 <-- Smaller Integer[/B] So (x, y) = (10, 12)
2m - n/3 = 5m for n
2m - n/3 = 5m for n Subtract 2m from each side of the equation: 2m-n/3 - 2m = 5m - 2m -n/3 = 3m Multiply each side of the equation by -3 to isolate n: -3 * -n/3 = -3 * 3m n = [B]-9m[/B]
2x decreased by 15 is equal to -27
2x decreased by 15 is equal to -27 The phrase [I]decreased by[/I] 15 means we subtract 15 from 2x: 2x - 15 The phrase [I]is equal to[/I] means an equation, so we set 2x - 15 equal to -27 [B]2x - 15 = -27 [/B] <-- This is our algebraic expression To solve this, [URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D-27&pl=Solve']type 2x - 15 = -27 into the search engine[/URL].
2x plus 4 increased by 15 is 57
2x plus 4 increased by 15 is 57 Take this algebraic expression in parts: [LIST] [*]2x plus 4: 2x + 4 [*][I]Increased by[/I] means we add 15 to 2x + 4: 2x + 4 + 15 = 2x + 19 [*]The word [I]is[/I] means an equation, so we set 2x + 19 equal to 57: [/LIST] Our final algebraic expression is: [B]2x + 19 = 57 [/B] To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B19%3D57&pl=Solve']type this equation into our search engine [/URL]and we get x = [B]19[/B]
2x^2+4x < 3x+6
2x^2+4x < 3x+6 Subtract 3x from both sides: 2x^2 + x < 6 Subtract 6 from both sides 2x^2 + x - 6 < 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=2x%5E2%2Bx-6&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: x < 1.5 and x < -2 When we take the intersection of these, it's [B]x < 1.5[/B]
3 adults and 4 children must pay $136. 2 adults and 3 children must pay $97.
3a + 4c = 136 2a + 3c = 97 [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=3a+%2B+4c+%3D+136&term2=2a+%2B+3c+%3D+97&pl=Cramers+Method']Using any of the 3 methods here[/URL]: [B]a = 20 c = 19[/B]
3 times a number is 3 more a number
3 times a number is 3 more a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 3 times a number: 3x 3 more than a number means we add 3 to x: x + 3 The word [I]is[/I] means and equation, so we set 3x equal to x + 3 [B]3x = x + 3[/B]
3 times the difference of a and b is equal to 4 times c
3 times the difference of a and b is equal to 4 times c [U]The difference of a and b:[/U] a - b [U]3 times the difference of a and b:[/U] 3(a - b) [U]4 times c:[/U] 4c The phrase [I]is equal to[/I] means an equation. So we set 3(a - b) equal to 4c: [B]3(a - b) = 4c[/B]
3 times the difference of x and 5 is 15
The difference of x and 5 means we subtract: x - 5 3 times the difference means we multiply (x - 5) by 3 3(x - 5) Is, means equal to, so we set our expression equal to 15 [B]3(x - 5) = 15 [/B] If you need to take it one step further to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3%28x-5%29%3D15&pl=Solve']equation calculator[/URL]
3 times x minus y is 5 times the sum of y and 2 times x
3 times x minus y is 5 times the sum of y and 2 times x Take this algebraic expression in pieces: 3 times x: 3x Minus y means we subtract y from 3x 3x - y The sum of y and 2 times x mean we add y to 2 times x y + 2x 5 times the sum of y and 2 times x: 5(y + 2x) The word [I]is[/I] means an equation, so we set 3x - y equal to 5(y + 2x) [B]3x - y = 5(y + 2x)[/B]
3 to the power of 2 times 3 to the power of x equals 3 to the power of 7
3 to the power of 2 times 3 to the power of x equals 3 to the power of 7. Write this out: 3^2 * 3^x = 3^7 When we multiply matching coefficients, we add exponents, so we have: 3^(2 + x) = 3^7 Therefore, 2 + x = 7. To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%2Bx%3D7&pl=Solve']type it into our search engine[/URL] and we get: x = [B]5[/B]
3 unknowns using Cramers Rule
Solves for 3 unknowns with equations in the form ax + by + cz = d using Cramers Method.
3-dimensional points
Calculates distance between two 3-dimensional points
(x1, y1, z1) and (x2, y2, z2) as well as the parametric equations and symmetric equations
3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the
3/5 of workers at a company have enrolled in the 403(b) program. If 24 workers have enrolled in the program, how many workers are employed at this company? We read this as 3/5 of the total workers employed at the company equals 24. Let w be the number of workers. We have the following equation: 3/5w = 24 Run [URL='http://www.mathcelebrity.com/1unk.php?num=3%2F5w%3D24&pl=Solve']3/5w = 24[/URL] through the search engine, we get [B]w = 40[/B].
30 is equal to thrice y decreased by z
30 is equal to thrice y decreased by z Thrice y means we multiply y by 3: 3y Decreased by z means we subtract z from 3y 3y - z The phrase [I]is[/I] means an equal to, so we set up an equation where 3y - z is equal to 30 [B]3y - z = 30[/B]
300 reduced by 5 times my age is 60
300 reduced by 5 times my age is 60 Let my age be a. We have: 5 times my age = 5a 300 reduced by 5 times my age means we subtract 5a from 300: 300 - 5a The word [I]is[/I] means an equation, so we set 300 - 5a equal to 60 to get our final algebraic expression: [B]300 - 5a = 60 [/B] If you have to solve for a, you [URL='https://www.mathcelebrity.com/1unk.php?num=300-5a%3D60&pl=Solve']type this equation into our search engine[/URL] and you get: a = [B]48[/B]
309 is the same as 93 subtracted from the quantity f times 123
309 is the same as 93 subtracted from the quantity f times 123. The quantity f times 123: 123f Subtract 93: 123f - 93 The phrase [I]is the same as[/I] means an equation, so we set 123f - 93 equal to 309 [B]123f - 93 = 309[/B] <-- This is our algebraic expression If you wish to solve for f, [URL='https://www.mathcelebrity.com/1unk.php?num=123f-93%3D309&pl=Solve']type this equation into the search engine[/URL], and we get f = 3.2683.
324 times z, reduced by 12 is z
324 times z, reduced by 12 is z. Take this algebraic expression in pieces: 324 [I]times[/I] z means we multiply 324 by the variable z. 324z [I]Reduced by[/I] 12 means we subtract 12 from 324z 324z - 12 The word [I]is[/I] means we have an equation, so we set 324z - 12 equal to z [B]324z - 12 = z [/B] <-- This is our algebraic expression
339 equals 303 times w, minus 293
339 equals 303 times w, minus 293 Take this algebraic expression in pieces: 303 times w: 303w Minus 293: 303w - 293 The phrase [I]equals[/I] means we have an equation. We set 303w - 293 = 339 [B]303w - 293 = 339[/B] <-- This is our algebraic expression To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=303w-293%3D339&pl=Solve']we type this equation into our search engine[/URL] to get: [B]w = 2.086[/B]
36% of the pupils in class 2 are boys the remaining 16 are girls how many pupils are in class 2?
36% of the pupils in class 2 are boys the remaining 16 are girls how many pupils are in class 2? This means 100% - 36% = 64% of the class are girls. And if the class size is s, then we have: 64% of s = 16 Or, written as a decimal: 0.64s = 16 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.64s%3D16&pl=Solve']type it into our search engine[/URL] and we get: s = [B]25[/B]
38 books into 8 boxes. 6 left. How many books in each box
38 books into 8 boxes. 6 left. How many books in each box Let the number of books in each box be b. We have the following relation: 8b + 6 = 38 to solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B6%3D38&pl=Solve']type it in our search engine[/URL] and we get: b = [B]4[/B]
3k^3 = rt for t
3k^3 = rt for t This is a literal equation. Let's divide each side of the equation by r, to isolate t: 3k^3/r = rt/r Cancel the r's on the right side, and we get: t = [B]3k^3/r[/B]
3timesanumberdecreasedby3
A necklace chain costs $15. Beads cost $2.50 each. You spend a total of $30 on a necklace and beads before tax. How many beads did you buy in addition to the necklace? Let the number of beads be b. We're given the following equation: 2.5b + 15 = 30 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5b%2B15%3D30&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]6[/B]
3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5
3x less than 2 times the sum of 2x and 1 is equal to the sum of 2 and 5 This is an algebraic expression. Let's take this algebraic expression in 5 parts: [LIST=1] [*]The sum of 2x and 1 means we add 1 to 2x: 2x + 1 [*]2 times the sum of 2x and 1: 2(2x + 1) [*]3x less than the sum of 2x and 1 means we subtract 3x from 2(2x + 1): 2(2x + 1) - 3x [*]The sum of 2 and 5 means we add 5 to 2: 2 + 5 [*]Finally, the phrase [I]equal[/I] means an equation, so we set #3 equal to #4 [/LIST] Our algebraic expression is: [B]2(2x + 1) - 3x = 2 + 5[/B] [B][/B] Now, some problems may ask you to simplify. In this case, we multiply through and group like terms: 4x + 2 - 3x = 7 [B]x + 2 = 7 <-- This is our simplified algebraic expression [/B] Now, what if the problem asks you to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B2%3D7&pl=Solve']you type this into our search engine[/URL] and get: x =[B] 5[/B]
4 minus 3p equals 36
4 minus 3p equals 36 4 minus 3p: 4 - 3p The phrase [I]equals[/I] means an equation, so we set 4 - 3p equal to 36: [B]4 - 3p = 36[/B]
4 times a number is the same as the number increased by 78
4 times a number is the same as the number increased by 78. Let's take this algebraic expression in parts: [LIST=1] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]4 times a number is written as 4x [*]The number increased by 78 means we add 78 to x: x + 78 [*]The phrase [I]the same as[/I] mean an equation, so we set #2 equal to #3 [/LIST] [B]4x = x + 78[/B] <-- This is our algebraic expression If the problem asks you to take it a step further, then [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3Dx%2B78&pl=Solve']we type this equation into our search engine [/URL]and get: x = 26
4 unknowns using Cramers Rule
Solves for 4 unknowns with equations in the form aw + bx + cy + dz = e using Cramers Method.
400 reduced by 3 times my age is 214
400 reduced by 3 times my age is 214 Let my age be a. We have: 3 times my age: 3a 400 reduced by 3 times my age: 400 - 3a The word [I]is[/I] means an equation. So we set 400 - 3a equal to 214 400 - 3a = 214 Now if you want to solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D214&pl=Solve']type it in the search engin[/URL]e and we get; a = [B]62[/B]
41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The rema
41% of the passengers on the plane are men. 36% of them are women and 11% of them are boys. The remaining 30 passengers are girls. How many passengers are on the plane? Add up the percents: 41% + 36% + 11% = 88% This means that (100% - 88% = 12%) are girls. So if the total amount of passengers on the plane is p, we write 12% s 0.12, and we have: 0.12p = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=0.12p%3D30&pl=Solve']Type this equation into our search engine[/URL], and we get: p = [B]250[/B]
414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost wa
414 people used public pool. Daily prices are $1.75 for children and $2.00 for adults. Total cost was $755.25. How many adults and children used the pool Let the number of children who used the pool be c, and the number of adults who used the pool be a. We're given two equations: [LIST=1] [*]a + c = 414 [*]2a + 1.75c = 755.25 [/LIST] We have a simultaneous equations. You can solve this any of 3 ways below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+414&term2=2a+%2B+1.75c+%3D+755.25&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] Whichever method you choose, you get the same answer: [LIST] [*][B]a = 123[/B] [*][B]c = 291[/B] [/LIST]
45 students, 12 taking spanish, 15 taking chemistry, 5 taking both spanish and chemistry. how many s
45 students, 12 taking spanish, 15 taking chemistry, 5 taking both spanish and chemistry. how many students are not taking either? Let S be the number of students taking spanish and C be the number of students taking chemistry: We have the following equation relating unions and intersections: P(C U S) = P(C) + P(S) - P(C and S) P(C U S) = 15 + 12 - 5 P(C U S) = 22 To get people that aren't taking either are, we have: 45 - P(C U S) 45 - 22 [B]23[/B]
450 people attended a concert at the center. the center was 3/4 full. what is the capacity of the mu
450 people attended a concert at the center. the center was 3/4 full. what is the capacity of the music center. Let the capacity be c. We're given: 3c/4 = 450 To solve this equation, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=450&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: c = [B]600[/B]
46 people showed up to the party. There were 8 less men than women present. How many men were there?
46 people showed up to the party. There were 8 less men than women present. How many men were there? Let the number of men be m. Let the number of women be w. We're given two equations: [LIST=1] [*]m = w - 8 [I](8 less men than women)[/I] [*]m + w = 46 [I](46 showed up to the party)[/I] [/LIST] Substitute equation (1) into equation (2) for m: w - 8 + w = 46 To solve for w in this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=w-8%2Bw%3D46&pl=Solve']type in the equation into our search engine [/URL]and we get: w = 27 To solve for men (m), we substitute w = 27 into equation (1): m = 27 - 8 m = [B]19[/B]
4subtractedfrom6timesanumberis32
4 subtracted from 6 times a number is 32. Take this algebraic expression in pieces. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 6 times this number means we multiply by x by 6 6x 4 subtracted from this expression means we subtract 4 6x - 4 The phrase [I]is[/I] means an equation, so we set 6x - 4 equal to 32 [B]6x - 4 = 32 [/B] If you need to solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=6x-4%3D32&pl=Solve']type it in the search engine here[/URL].
5 -8| -2n|=-75
Subtract 5 from each side: -8|-2n| = -80 Divide each side by -8 |-2n| = 10 Since this is an absolute value equation, we need to setup two equations: -2n = 10 -2n = -10 Solving for the first one by dividing each side by -2, we get: n = -5 Solving for the second one by dividing each side by -2, we get: n = 5
5 books and 5 bags cost $175. What is the cost of 2 books and 2 bags
5 books and 5 bags cost $175. What is the cost of 2 books and 2 bags Let the cost of each book be b and the cost of each bag be c. We're given 5b + 5c = 175 We can factor this as: 5(b + c) = 175 Divide each side of the equation by 5, we get: (b + c) = 35 The problem asks for 2b + 2c Factor out 2: 2(b + c) we know from above that (b + c) = 35, so we substitute: 2(35) [B]70[/B]
5 subtracted from 3 times a number is 44
5 subtracted from 3 times a number is 44. The problem asks for an algebraic expression. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. 3 times this number is 3x. 5 subtracted from this is written as 3x - 5. The phrase [I]is[/I] means an equation, so we set 3x - 5 equal to 44 [B]3x - 5 = 44[/B]
5 times a number is that number minus 3
5 times a number is that number minus 3 The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. [LIST] [*]5 times a number: 5x [*]That number means we use the same number from above which is x [*]That number minus 3: x - 3 [*]The phrase [I]is[/I] means an equation, so we set 5x equal to x - 3 [/LIST] [B]5x = x - 3[/B]
5 years ago Kevin was 3 times as old as Tami. Now he is twice as old as she is. How is each now?
5 years ago Kevin was 3 times as old as Tami. Now he is twice as old as she is. How is each now? Let Kevin's age be k. Let Tami's age be t. We're given the following equations: [LIST=1] [*]k - 5 = 3(t - 5) [*]k = 2t [/LIST] Plug equation (2) into equation (1) for k: 2t - 5 = 3(t - 5) We p[URL='https://www.mathcelebrity.com/1unk.php?num=2t-5%3D3%28t-5%29&pl=Solve']lug this equation into our search engine[/URL] and we get: t = [B]10. Tami's age[/B] Now plug t = 10 into equation (2) to solve for k: k = 2(10) k =[B] 20. Kevin's age[/B]
5000 union members of a financially troubled company accepted a 17% pay cut. The company announced t
5000 union members of a financially troubled company accepted a 17% pay cut. The company announced that this would save them approximately $108 million annually. Based on this information, calculate the average annual pay of a single union member Let the full salary of the union members be s. Since 17% is 0.17, We're given: 0.17s = 108000000 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.17s%3D108000000&pl=Solve']type it in our search engine[/URL] and we get: s = 635,294,117.65 Calculate the average annual pay of a single union member: Average Pay = Total Pay / Number of Union Members Average Pay = 635,294,117.65 / 5000 Average Pay = [B]127,058.82[/B]
508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $
508 people are there, the daily price is $1.25 for kids and $2.00 for adults. The receipts totaled $885.50. How many kids and how many adults were there? Assumptions: [LIST] [*]Let the number of adults be a [*]Let the number of kids be k [/LIST] Given with assumptions: [LIST=1] [*]a + k = 508 [*]2a + 1.25k = 885.50 (since cost = price * quantity) [/LIST] Rearrange equation (1) by subtracting c from each side to isolate a: [LIST=1] [*]a = 508 - k [*]2a + 1.25k = 885.50 [/LIST] Substitute equation (1) into equation (2): 2(508 - k) + 1.25k = 885.50 Multiply through: 1016 - 2k + 1.25k = 885.50 1016 - 0.75k = 885.50 To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=1016-0.75k%3D885.50&pl=Solve']type this equation into our search engine[/URL] and we get: k = [B]174[/B] Now, to solve for a, we substitute k = 174 into equation 1 above: a = 508 - 174 a = [B]334[/B]
54 is the sum of 15 and Vidyas score
54 is the sum of 15 and Vidyas score. Let Vida's score be s. The sum of 15 and s: s + 15 When they say "is", they mean equal to, so we set s + 15 equal to 54. Our algebraic expression is below: [B]s + 15 = 54 [/B] To solve this equation for s, use our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B15%3D54&pl=Solve']equation calculator[/URL]
54 is the sum of 24 and Julies score. Use the variable J to represent Julies score.
54 is the sum of 24 and Julies score. Use the variable J to represent Julies score. Sum of 24 and Julie's score: 24 + J The phrase [I]is[/I] means an equation, so we set 24 + J equal to 54 to get an algebraic expression: [B]24 + J = 54[/B]
59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving.
59 is the sum of 16 and Donnie's saving. Use the variable d to represent Donnie's saving. The phrase [I]the sum of[/I] means we add Donnie's savings of d to 16: d + 16 The phrase [I]is[/I] means an equation, so we set d + 16 equal to 59 d + 16 = 59 <-- [B]This is our algebraic expression[/B] Now, if the problem asks you to solve for d, then you[URL='https://www.mathcelebrity.com/1unk.php?num=d%2B16%3D59&pl=Solve'] type the algebraic expression into our search engine to get[/URL]: d = [B]43[/B]
5y^0=15x for y
5y^0=15x for y y^0 = 1, so we have: 5(1) = 15x 5 = 15x To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%3D15x&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]1/3[/B]
6 numbers have a mean of 4. What is the total of the 6 numbers?
6 numbers have a mean of 4. What is the total of the 6 numbers? Mean = Sum of numbers / Count of numbers Plug our Mean of 4 and our count of 6 into this equation: 4 = Sum/Total of Numbers / 6 Cross multiply: Sum/Total of Numbers = 6 * 4 Sum/Total of Numbers = [B]24[/B]
6 subtracted from the product of 5 and a number is 68
6 subtracted from the product of 5 and a number is 68 Take this algebraic expression in parts. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The product of 5 and this number is: 5x We subtract 6 from 5x: 5x - 6 The phrase [I]is[/I] means an equation, so we set 5x - 6 equal to 68 [B]5x - 6 = 68[/B]
6 times the reciprocal of a number equals 3 times the reciprocal of 7 .
6 times the reciprocal of a number equals 3 times the reciprocal of 7 . This is an algebraic expression. Let's take it in parts: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The reciprocal of a number x means we divide 1 over x: 1/x 6 times the reciprocal means we multiply 6 by 1/x: 6/x The reciprocal of 7 means we divide 1/7 1/7 3 times the reciprocal means we multiply 1/7 by 3: 3/7 Now, the phrase [I]equals[/I] mean an equation, so we set 6/x = 3/7 [B]6/x = 3/7[/B] <-- This is our algebraic expression If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/prop.php?num1=6&num2=3&den1=x&den2=7&propsign=%3D&pl=Calculate+missing+proportion+value']we type this proportion in our search engine[/URL] and get: x = 14
6 times the sum of a number and 3 is equal to 42. What is this number?
6 times the sum of a number and 3 is equal to 42. What is this number? The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The sum of a number and 3 means we add 3 to x: x + 3 6 times the sum: 6(x + 3) The word [I]is[/I] means an equation, so we set 6(x + 3) equal to 42 to get our [I]algebraic expression[/I] of: [B]6(x + 3) = 42[/B] [B][/B] If the problem asks you to solve for x, then [URL='https://www.mathcelebrity.com/1unk.php?num=6%28x%2B3%29%3D42&pl=Solve']you type this equation into our search engine[/URL] and you get: x = [B]4[/B]
6 years from now Cindy will be 25 years old. in 12 years, the sum of the ages of Cindy and Jose will
6 years from now Cindy will be 25 years old. in 12 years, the sum of the ages of Cindy and Jose will be 91. how old is Jose right now? Let c be Cindy's age and j be Jose's age. We have: c + 6 = 25 This means c = 19 using our [URL='https://www.mathcelebrity.com/1unk.php?num=c%2B6%3D25&pl=Solve']equation calculator[/URL]. We're told in 12 years, c + j = 91. If Cindy's age (c) is 19 right now, then in 12 years, she'll be 19 + 12 = 31. So we have 31 + j = 91. Using our [URL='https://www.mathcelebrity.com/1unk.php?num=31%2Bj%3D91&pl=Solve']equation calculator[/URL], we get [B]j = 60[/B].
60 percent of a number minus 17 is -65
60 percent of a number minus 17 is -65 Using our [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=60&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']percent to decimal calculator[/URL], we see that 60% is 0.6, so we have: 0.6 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So 60% of a number is: 0.6x Minus 17: 0.6x - 17 The word [I]is[/I] means an equation, so we set 0.6x - 17 equal to -65 to get our algebraic expression of: [B]0.6x - 17 = -65[/B] [B][/B] If you want to solve for x in this equation, you [URL='https://www.mathcelebrity.com/1unk.php?num=0.6x-17%3D-65&pl=Solve']type it in our search engine and you get[/URL]: [B]x = -80[/B]
63 is the sum of 24 and helenas age
Set up an equation where h is Helena's age. h + 24 = 63 [URL='http://www.mathcelebrity.com/1unk.php?num=h%2B24%3D63&pl=Solve']Subtract 24 from each side[/URL] h = 39
64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44.
64 is 4 times the difference between Sarah's age, a, and 44. Assume Sarah is older than 44. The phrase [I]difference between[/I] means we subtract 44 from a: a - 44 The phrase [I]64 is[/I] means an equation, so we set a - 44 equal to 64 [B]a - 44 = 64 <-- This is our algebraic expression [/B] If you want to solve for a, then we [URL='https://www.mathcelebrity.com/1unk.php?num=a-44%3D64&pl=Solve']type this expression into our search engine[/URL] and get: [B]a = 108[/B]
64 is 4 times the difference between Sarah�s age a, and 44.Assume Sarah is older than 44
64 is 4 times the difference between Sarah�s age a, and 44.Assume Sarah is older than 44 Difference between Sarah's age (a) and 44 (Assuming Sarah is older than 44): a - 44 4 times the difference: 4(a - 44) The word [I]is[/I] means equal to, so we set 4(a - 44) equal to 64 to get our algebraic expression: [B]4(a - 44) = 64[/B] If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4%28a-44%29%3D64&pl=Solve']type this equation into our search engine[/URL] and we get: a = [B]60[/B]
7 and 105 are successive terms in a geometric sequence. what is the term following 105?
7 and 105 are successive terms in a geometric sequence. what is the term following 105? Geometric sequences are set up such that the next term in the sequence equals the prior term multiplied by a constant. Therefore, we express the relationship in the following equation: 7k = 105 where k is the constant [URL='https://www.mathcelebrity.com/1unk.php?num=7k%3D105&pl=Solve']Type this equation into our search engine[/URL] and we get: k = 15 The next term in the geometric sequence after 105 is found as follows: 105*15 = [B]1,575[/B]
7 is 1/4 of some number
7 is 1/4 of some number The phrase [I]some number[/I] means an arbitrary variable, let's call it x. 1/4 of this is written as: x/4 The word [I]is[/I] means an equation, so we set x/4 equal to 7: [B]x/4 = 7[/B]
7 times a number and 2 is equal to 4 times a number decreased by 8
7 times a number and 2 is equal to 4 times a number decreased by 8 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 7 times a number: 7x and 2 means we add 2: 7x + 2 4 times a number 4x decreased by 8 means we subtract 8: 4x - 8 The phrase [I]is equal to[/I] means an equation, so we set 7x + 2 equal to 4x - 8: [B]7x + 2 = 4x - 8[/B]
7 times a number is the same as 12 more than 3 times a number
7 times a number is the same as 12 more than 3 times a number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [B][U]Algebraic Expression 1:[/U][/B] 7 times a number means we multiply 7 by x: 7x [B][U]Algebraic Expression 2:[/U][/B] 3 times a number means we multiply 3 by x: 3x 12 more than 3 times a number means we add 12 to 3x: 3x + 12 The phrase [I]is the same as[/I] means an equation, so we set 7x equal to 3x + 12 [B]7x = 3x + 12[/B] <-- Algebraic Expression
75% of a ship�s cargo was destroyed by an on-board fire. The captain of the ship sold the remaining
75% of a ship�s cargo was destroyed by an on-board fire. The captain of the ship sold the remaining cargo, which was slightly damaged, for 25% of its real value and received $1400. What was the value of the cargo before the fire? (Do not include the $ sign or commas in the answer) So 25% of the cargo is left. This was sold at 25% of value. Let the starting value be s: We have 0.25 * 0.25 * s = 1400 0.0625s = 1400 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.0625s%3D1400&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]22400[/B]
75% of x is 25 dollars and 99 cents
75% of x is 25 dollars and 99 cents [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=+90&den1=+80&pct=75&pcheck=4&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']Since 75%[/URL] is 0.75 as a decimal, we rewrite this as an algebraic expression: 0.75x = 25.99 If we want to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75x%3D25.99&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]34.65[/B]
76 subtracted from p is equal to the total of g and 227
76 subtracted from p is equal to the total of g and 227 We've got two algebraic expressions. Take them in pieces: Part 1: 76 subtracted from p We subtract 76 from the variable p p - 76 Part 2: The total of g and 227 The total means a sum, so we add 227 to g g + 227 Now the last piece, the phrase [I]is equal to[/I] means an equation. So we set both algebraic expressions equal to each other: [B]p - 76 = g + 227[/B]
8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is
8 times the difference of a number and 2 is the same as 3 times the sum of the number and 3. What is the number? Let the number be n. We're given two expressions: [LIST=1] [*]8(n - 2) [I]difference means we subtract[/I] [*]3(n + 3) [I]sum means we add[/I] [/LIST] The phrase [I]is the same as[/I] mean an equation. So we set the first expression equal to the second expression: 8(n - 2) = 3(n + 3) To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=8%28n-2%29%3D3%28n%2B3%29&pl=Solve']type it in our search engine[/URL] and we see that: n =[B] 5[/B]
8 years from now a girls age will be 5 times her present age whats is the girls age now
8 years from now a girls age will be 5 times her present age whats is the girls age now. Let the girl's age now be a. We're given: a + 8 = 5a [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D5a&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]a = 2[/B]
9 divided by the sum of x and 4 is equal to 6 divided by x minus 4
9 divided by the sum of x and 4 is equal to 6 divided by x minus 4. Build our two algebraic expressions first: 9 divided by the sum of x and 4 9/(x + 4) 6 divided by x minus 4 6/(x - 4) The phrase [I]is equal to[/I] means and equation, so we set the algebraic expressions equal to each other: [B]9/(x + 4) = 6/(x - 4) <-- This is our algebraic expression[/B] [B][/B] If the problem asks you to solve for x, we cross multiply: 9(x - 4) = 6(x + 4) To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%28x-4%29%3D6%28x%2B4%29&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]20[/B]
9 is one-third of a number x
9 is one-third of a number x A number x can be written as x x one-third of a number x means we multiply x by 1/3: x/3 The phrase [I]is[/I] means an equation, so we set 9 equal to x/3 to get our final algebraic expression of: [B]x/3 = 9[/B] If the problem asks you to solve for x, you [URL='https://www.mathcelebrity.com/prop.php?num1=x&num2=9&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this algebraic expression into our search engine[/URL] and you get: [B]x = 27[/B]
9 less than 5 times a number is 3 more than 2x
9 less than 5 times a number is 3 more than 2x The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x 5 times a number means we multiply x by 5: 5x 9 less than 5x means we subtract 9 from 5x: 5x - 9 3 more than 2x means we add 3 to 2x: 2x + 3 The word [I]is[/I] means an equation, so we set 5x - 9 equal to 2x + 3: [B]5x - 9 = 2x + 3 <-- This is our algebraic expression[/B] [B][/B] If you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=5x-9%3D2x%2B3&pl=Solve']type this equation into the search engine[/URL], and we get: x = [B]4[/B]
9 times a number is that number minus 3
9 times a number is that number minus 3 Let [I]a number[/I] be an arbitrary variable, let's call it x. We're given: 9 times a number is 9x The number minus 3 is x - 3 The word [I]is[/I] means an equation, so we set 9x equal to x - 3 to get our [I]algebraic expression[/I]: [B]9x = x - 3[/B] To solve for x, we type this equation into our search engine and we get: x = [B]-0.375 or -3/8[/B]
963 animals on a farm, 159 sheep and 406 cows and pigs. How many are pigs?
963 animals on a farm, 159 sheep and 406 cows and pigs. How many are pigs? Set up equation to represent the total animals on the farm Total Animals = Cows + Pigs + Sheep Now plug in what is given 963 = 406 + Pigs + 159 Simplify: Pigs + 565 = 963 Subtract 565 from each side [B]Pigs = 398[/B]
993 cold drinks bottles are to be placed in crates. Each crate can hold 9 bottles. How many crates w
993 cold drinks bottles are to be placed in crates. Each crate can hold 9 bottles. How many crates would be needed and how many bottles will remain? Let c equal the number of crates 9 bottles per crate * c = 993 9c = 993 Solve for [I]c[/I] in the equation 9c = 993 [SIZE=5][B]Step 1: Divide each side of the equation by 9[/B][/SIZE] 9c /9 = 993/9 c = 110.33333333333 Since we can't have fractional crates, we round up 1 to the next full crate c = [B]111[/B]
A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percen
A $480 TV was put on sale for 30% off. It didn't sell, so the price was lowered an additional percent off the sale price, making the new sale price $285.60. What was the second percent discount that was given? Let the second discount be d. We're given: 480 * (1 - 0.3)(1 - d) = 285.60 480(0.7)(1 - d) = 285.60 336(1 - d) = 285.60 336 - 336d = 285.60 [URL='https://www.mathcelebrity.com/1unk.php?num=336-336d%3D285.60&pl=Solve']Type this equation into our search engine[/URL] to solve for d and we get: d = [B]0.15 or 15%[/B]
A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation
A $654,000 property is depreciated for tax purposes by its owner with the straight-line depreciation method. The value of the building, y, after x months of use is given by y = 654,000 ? 1800x dollars. After how many months will the value of the building be $409,200? We want to know x for the equation: 654000 - 1800x = 409200 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=654000-1800x%3D409200&pl=Solve']type it in our math engine[/URL] and we get: x = [B]136 months[/B]
A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x repre
A $675 stereo receiver loses value at a rate of about $18 per month The equation y = 675 - 18x represents the value of the receiver after x months. Identify and interpret the x- and y-intercepts. Explain how you can use the intercepts to help you graph the equation y = 675 - 18x The y-intercept is found when x is 0: y = 675 - 18(0) y = 675 - 0 y = 675 The x-intercept is found when y is 0: 0 = 675 - 18x [URL='https://www.mathcelebrity.com/1unk.php?num=675-18x%3D0&pl=Solve']Typing this equation into our search engine[/URL], we get: x = 37.5
a +?b +?c =?180 for b
a +?b +?c =?180 for b We have a literal equation. Subtract (a + c) from each side of the equation to isolate b: a + b + c - (a + c) = 180 - (a + c) The (a + c) cancels on the left side, so we have: [B]b = 180 - (a + c)[/B] or, distributing the negative sign: [B]b = 180 - a - c[/B]
A 12% acid solution is made by mixing 8% and 20% solutions. If the 450 ml of the 12% solution is req
A 12% acid solution is made by mixing 8% and 20% solutions. If the 450 ml of the 12% solution is required, how much of each solution is required? Component Unit Amount 8% Solution: 0.08 * x = 0.08x 20% Solution: 0.2 * y = 0.2y 12% Solution: 0.12 * 450 = 54 We add up the 8% solution and 20% solution to get two equations: [LIST=1] [*]0.08x + 0.2y = 54 [*]x + y = 450 [/LIST] We have a simultaneous set of equations. We can solve it using three methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.08x+%2B+0.2y+%3D+54&term2=x+%2B+y+%3D+450&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]x = 300 ml[/B] [*][B]y = 150 ml[/B] [/LIST]
A 15 feet piece of string is cut into two pieces so that the longer piece is 3 feet longer than twic
A 15 feet piece of string is cut into two pieces so that the longer piece is 3 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces. If the shorter piece is x, the longer piece is 20 - x We also are given 15 - x = 2x + 3 Add x to each side: 3x + 3 = 15 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B3%3D15&pl=Solve']equation calculator[/URL], we get a shorter piece of: [B]x = 4[/B] The longer piece is: 15 - x 15 - 4 [B]11[/B]
A 20 feet piece of string is cut into two pieces so that the longer piece is 5 feet longer than twic
A 20 feet piece of string is cut into two pieces so that the longer piece is 5 feet longer than twice the shorter piece. If the shorter piece is x feet long, find the lengths of both pieces. If the shorter piece is x, the longer piece is 20 - x We also are given 20 - x = 2x + 5 Add x to each side: 3x + 5 = 20 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B5%3D20&pl=Solve']equation calculator[/URL], we get a shorter piece of: [B]x = 5 [/B] The longer piece is: 20 - x 20 - 5 [B]15[/B]
A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an ho
A 3 hour river cruise goes 15 km upstream and then back again. The river has a current of 2 km an hour. What is the boat's speed and how long was the upstream journey? [U]Set up the relationship of still water speed and downstream speed[/U] Speed down stream = Speed in still water + speed of the current Speed down stream = x+2 Therefore: Speed upstream =x - 2 Since distance = rate * time, we rearrange to get time = Distance/rate: 15/(x+ 2) + 15 /(x- 2) = 3 Multiply each side by 1/3 and we get: 5/(x + 2) + 5/(x - 2) = 1 Using a common denominator of (x + 2)(x - 2), we get: 5(x - 2)/(x + 2)(x - 2) + 5(x + 2)/(x + 2)(x - 2) (5x - 10 + 5x + 10)/5(x - 2)/(x + 2)(x - 2) 10x = (x+2)(x-2) We multiply through on the right side to get: 10x = x^2 - 4 Subtract 10x from each side: x^2 - 10x - 4 = 0 This is a quadratic equation. To solve it, [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-10x-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine[/URL] and we get: Speed of the boat in still water =X=5 +- sq. Root of 29 kmph We only want the positive solution: x = 5 + sqrt(29) x = 10.38 [U]Calculate time for upstream journey:[/U] Time for upstream journey = 15/(10.38 - 2) Time for upstream journey = 15/(8.38) Time for upstream journey = [B]1.79[/B] [U]Calculate time for downstream journey:[/U] Time for downstream journey = 15/(10.38 + 2) Time for downstream journey = 15/(12.38) Time for downstream journey = [B]1.21[/B]
A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the ot
A 98-inch piece of wire must be cut into two pieces. One piece must be 10 inches shorter than the other. How long should the pieces be? The key phrase in this problem is [B]two pieces[/B]. Declare Variables: [LIST] [*]Let the short piece length be s [*]Let the long piece length be l [/LIST] We're given the following [LIST=1] [*]s = l - 10 [*]s + l = 98 (Because the two pieces add up to 98) [/LIST] Substitute equation (1) into equation (2) for s: l - 10+ l = 98 Group like terms: 2l - 10 = 98 Solve for [I]l[/I] in the equation 2l - 10 = 98 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 98. To do that, we add 10 to both sides 2l - 10 + 10 = 98 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] 2l = 108 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2l/2 = 108/2 l = [B]54[/B] To solve for s, we substitute l = 54 into equation (1): s = 54 - 10 s = [B]44[/B] Check our work: The shorter piece is 10 inches shorter than the longer piece since 54 - 44 = 10 Second check: Do both pieces add up to 98 54 + 44 ? 98 98 = 98
a = v^2/r for r
a = v^2/r for r Start by cross multiplying to get r out of the denominator: ar = v^2 Divide each side of the equation by a to isolate r: ar/a = v^2/a Cancel the a's on the left side, and we get: r = [B]v^2/a[/B]
A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every
A bag contains 120 marbles. Some are red and the rest are black. There are 19 red marbles for every black marble. How many red marbles are in the bag? Let the red marbles be r Let the black marbles be b. A 19 to 1 red to black is written as: r = 19b We're also given: b + r = 120 Substitute r = 19b into this equation and we get: b + 19b = 120 Combine like terms: 20b = 120 To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=20b%3D120&pl=Solve']we type it in our search engine [/URL]and we get: b = 6 Since r = 19b, we substitute b = 6 into this equation to solve for r: r = 19(6) r = [B]114[/B]
A bag of quarters and nickels is worth $8.30. There are two less than three times as many quarters a
A bag of quarters and nickels is worth $8.30. There are two less than three times as many quarters as nickels. How many of the coins must be quarters? Assumptions and givens: [LIST] [*]Let the number of quarters be q [*]Let the number of nickels be n [/LIST] We have two equations: [LIST=1] [*]0.05n + 0.25q = 8.30 [*]n = 3q - 2 [I](Two less than Three times)[/I] [/LIST] Plug in equation (2) into equation (1) for q to solve this system of equations: 0.05(3q - 2) + 0.25q = 8.30 To solve this equation for q, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.05%283q-2%29%2B0.25q%3D8.30&pl=Solve']type it in our search engine[/URL] and we get: q = [B]21[/B]
A bamboo tree grew 3 inches per day. How many days will it take the tree to grow 144 inches? Choose
A bamboo tree grew 3 inches per day. How many days will it take the tree to grow 144 inches? Choose the correct equation to represent this situation. Let the number of days be d. We have the equation: 3d = 144 To solve this equation for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=3d%3D144&pl=Solve']type it in our search engine[/URL] and we get: d = [B]48[/B]
A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a func
A baseball card that was valued at $100 in 1970 has increased in value by 8% each year. Write a function to model the situation the value of the card in 2020.Let x be number of years since 1970 The formula for accumulated value of something with a percentage growth p and years x is: V(x) = Initial Value * (1 + p/100)^x Set up our growth equation where 8% = 0.08 and V(y) for the value at time x and x = 2020 - 1970 = 50, we have: V(x) = 100 * (1 + 8/100)^50 V(x) = 100 * (1.08)^50 V(x) = 100 * 46.9016125132 V(x) = [B]4690.16[/B]
a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bri
a baseball player has 9 hits in his first 60 at bats. how many consecutive hits would he need to bring his average up to 0.400? Let the amount of consecutive hits needed be h. We have: hits / at bats = Batting Average Plugging in our numbers, we get: (9 + h)/60 = 0.400 Cross multiply: 9 + h = 60 * 0.4 9 + h = 24 To solve this equation for h, [URL='https://www.mathcelebrity.com/1unk.php?num=9%2Bh%3D24&pl=Solve']we type it in our search engine[/URL] and we get: h = [B]15[/B]
A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The ave
A bicycle store costs $1500 per month to operate. The store pays an average of $60 per bike. The average selling price of each bicycle is $80. How many bicycles must the store sell each month to break even? Profit = Revenue - Cost Let the number of bikes be b. Revenue = 80b Cost = 60b + 1500 Break even is when profit equals 0, which means revenue equals cost. Set them equal to each other: 60b + 1500 = 80b We [URL='https://www.mathcelebrity.com/1unk.php?num=60b%2B1500%3D80b&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]75[/B]
A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The a
A bicycle store costs $2750 per month to operate. The store pays an average of $45 per bike. The average selling price of each bicycle is $95. How many bicycles must the store sell each month to break even? Let the number of bikes be b. Set up our cost function, where it costs $45 per bike to produce C(b) = 45b Set up our revenue function, where we earn $95 per sale for each bike: R(b) = 95b Set up our profit function, which is how much we keep after a sale: P(b) = R(b) - C(b) P(b) = 95b - 45b P(b) = 50b The problem wants to know how many bikes we need to sell to break-even. Note: break-even means profit equals operating cost, which in this case, is $2,750. So we set our profit function of 50b equal to $2,750 50b = 2750 [URL='https://www.mathcelebrity.com/1unk.php?num=50b%3D2750&pl=Solve']We type this equation into our search engine[/URL], and we get: b = [B]55[/B]
A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the
A bird was sitting 12 meters from the base of an oak tree and flew 15 meters to reach the top of the tree. How tall is the tree? So we have a [U]right triangle[/U]. Hypotenuse is 15. Base is 12. We want the length of the leg. The formula for a right triangle relation of sides is a^2 + b^2 = c^2 where c is the hypotenuse and a, b are the sides Rearranging this equation to isolate a, we get a^2 = c^2 - b^2 Taking the square root of both sides, we get a = sqrt(c^2 - b^2) a = sqrt(15^2 - 12^2) a = sqrt(225 - 144) a = sqrt(81) a = [B]9 meters[/B]
A boa constrictor is 18 inches long at birth and grows 8 inches per year. Write an equation that rep
A boa constrictor is 18 inches long at birth and grows 8 inches per year. Write an equation that represents the length y (in feet) of a boa constrictor that is x years old. 8 inches per year = 8/12 feet = 2/3 foot [B]y = 18 + 2/3x[/B]
A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat t
A boat can carry 582 passengers to the base of a waterfall. A total of 13,105 people ride the boat today. All the rides are full except for the first ride. How many rides are given? 582 passengers on the boat Let r be the number of rides So we want to find r when: 582r = 13105 To solve for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=582r%3D13105&pl=Solve']type this equation into our math engine[/URL] and we get: r = 22.517 If we round this down, setting 0.517 rides as the first ride, we get: r = [B]22 [MEDIA=youtube]0J2YRPzKsoU[/MEDIA][/B]
a boat traveled 336 km downstream with the current. The trip downstream took 12 hours. write an equa
a boat traveled 336 km downstream with the current. The trip downstream took 12 hours. write an equation to describe this relationship We know the distance (d) equation in terms of rate (r) and time (t) as: d = rt We're given d = 336km and t = 12 hours, so we have: [B]336 km = 12t [/B] <-- this is our equation Divide each side by 12 to solve for t: 12t/12 = 336/12 t = [B]28 km / hour[/B]
A Bouquet of lillies and tulips has 12 flowers. Lillies cost $3 each, and tulips cost $2 each. The b
A Bouquet of lillies and tulips has 12 flowers. Lillies cost $3 each, and tulips cost $2 each. The bouquet costs $32. Write and solve a system of linear equations to find the number of lillies and tulips in the bouquet. Let l be the number of lillies and t be the number of tulips. We're given 2 equations: [LIST=1] [*]l + t = 12 [*]3l + 2t = 32 [/LIST] With this system of equations, we can solve it 3 ways. [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+t+%3D+12&term2=3l+%2B+2t+%3D+32&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter which method we choose, we get: [LIST] [*][B]l = 8[/B] [*][B]t = 4[/B] [/LIST] [B]Now Check Your Work For Equation 1[/B] l + t = 12 8 + 4 ? 12 12 = 12 [B]Now Check Your Work For Equation 2[/B] 3l + 2t = 32 3(8) + 2(4) ? 32 24 + 8 ? 32 32 = 32
A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils.
A box had x pencils. Then 6 pencils were removed from the box. The box now has 54 pencils. Removed means we subtract from the total. So Our equation is: x - 6 = 54 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-6%3D54&pl=Solve']type it in our search engine [/URL]and we get: x = [B]60[/B]
A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find th
A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each? Let the boy's age be b and his brother's age be c. We're given two equations: [LIST=1] [*]b = c + 10 [*]b + 4 = 2(c + 4) [/LIST] Substitute equation (1) into equation (2): (c + 10) + 4 = 2(c + 4) Simplify by multiplying the right side through and grouping like terms: c + 14 = 2c + 8 [URL='https://www.mathcelebrity.com/1unk.php?num=c%2B14%3D2c%2B8&pl=Solve']Type this equation into our search engine[/URL] and we get: c = [B]6[/B] Now plug c = 6 into equation (1): b = 6 + 10 b = [B]16[/B]
A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their pre
A boy is 6 years older than his sister. In 3 years time he will be twice her age. What are their present ages? Let b be the boy's age and s be his sister's age. We're given two equations: [LIST=1] [*]b = s + 6 [*]b + 3 = 2(s + 3) [/LIST] Plug in (1) to (2): (s + 6) + 3 = 2(s + 3) s + 9 = 2s + 6 [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B9%3D2s%2B6&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]s = 3[/B] We plug s = 3 into Equation (1) to get the boy's age (b): b = 3 + 6 [B]b = 9[/B]
a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that
a boy purchased a party-length sandwich 57 inches long. he wants to cut it into three pieces so that the middle piece is 6inches longer than the shortest piece and the shortest piece is 9 inches shorter than the longest price. how long should the three pieces be? Let the longest piece be l. The middle piece be m. And the short piece be s. We have 2 equations in terms of the shortest piece: [LIST=1] [*]l = s + 9 (Since the shortest piece is 9 inches shorter, this means the longest piece is 9 inches longer) [*]m = s + 6 [*]s + m + l = 57 [/LIST] We substitute equations (1) and (2) into equation (3): s + (s + 6) + (s + 9) = 57 Group like terms: (1 + 1 + 1)s + (6 + 9) = 57 3s + 15 = 57 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3s%2B15%3D57&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]14 [/B] [U]Plug s = 14 into equation 2 to solve for m:[/U] m = 14 + 6 m = [B]20 [/B] [U]Plug s = 14 into equation 1 to solve for l:[/U] l = 14 + 9 l = [B]23 [/B] Check our work for equation 3: 14 + 20 + 23 ? 57 57 = 57 <-- checks out [B][/B]
A brand new car that is originally valued at $25,000 depreciates by 8% per year. What is the value o
A brand new car that is originally valued at $25,000 depreciates by 8% per year. What is the value of the car after 6 years? The Book Value depreciates 8% per year. We set up a depreciation equation: BV(t) = BV(0) * (1 - 0.08)^t The Book Value at time 0 BV(0) = 25,000. We want the book value at time 6. BV(6) = 25,000 * (1 - 0.08)^6 BV(6) = 25,000 * 0.92^6 BV(6) = 25,000 * 0.606355 BV(6) = [B]15,158.88[/B]
A bus is carrying 135 passengers, which is 3/4 of the capacity of the bus. What is the capacity of t
A bus is carrying 135 passengers, which is 3/4 of the capacity of the bus. What is the capacity of the bus Let the capacity of the bus be c. We're given: 3c/4 = 135 To solve for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=135&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type this equation into our search engine [/URL]and we get: c = [B]180[/B]
A business owner spent $4000 for a computer and software. For bookkeeping purposes, he needs to post
A business owner spent $4000 for a computer and software. For bookkeeping purposes, he needs to post the price of the computer and software separately. The computer costs 4 times as much as the software. What is the cost of the software? Let c be the cost of the computer and s be the cost of the software. We have two equations: [LIST=1] [*]c + s = 4000 [*]c = 4s [/LIST] Substitute (2) into (1) (4s) + s = 4000 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2Bs%3D4000&pl=Solve']equation solver[/URL], we get [B]s = 800[/B]. Substitute this into Equation (2), we get: c = 4(800) [B]c = 3,200[/B]
A cab company charges $5 per cab ride, plus an additional $1 per mile driven , How long is a cab rid
A cab company charges $5 per cab ride, plus an additional $1 per mile driven , How long is a cab ride that costs $13? Let the number of miles driven be m. Our cost function C(m) is: C(m) = Cost per mile * m + cab cost C(m) = 1m + 5 The problem asks for m when C(m) = 13: 1m + 5 = 13 To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=1m%2B5%3D13&pl=Solve']we type it in our search engine[/URL] and we get: m = [B]8[/B]
A cab company charges $5 per cab ride, plus an additional $3 per mile driven. How long is a cab ride
A cab company charges $5 per cab ride, plus an additional $3 per mile driven. How long is a cab ride that costs $17? Let m be the number of miles driven. We setup the cost equation C(m): C(m) = Cost per mile driven * miles driven + ride cost C(m) = 3m + 5 The questions asks for m when C(m) is 17: 3m + 5 = 17 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%2B5%3D17&pl=Solve']type it in our search engine[/URL] and we get: m = [B]4[/B]
A cable company charges $75 for installation plus $20 per month. Another cable company offers free i
A cable company charges $75 for installation plus $20 per month. Another cable company offers free installation but charges $35 per month. For how many months of cable service would the total cost from either company be the same [U]Set ups the cost function for the first cable company C(m) where m is the number of months:[/U] C(m) = cost per month * m + installation fee C(m) = 20m + 75 [U]Set ups the cost function for the second cable company C(m) where m is the number of months:[/U] C(m) = cost per month * m + installation fee C(m) = 35m The problem asks for m when both C(m) functions are equal. So we set both C(m) functions equal and solve for m: 20m + 75 = 35m To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B75%3D35m&pl=Solve']type this equation into our search engine[/URL] and we get: m = [B]5[/B]
A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the can
A candlestick burns at a rate of 0.2 inches per hour. After eight straight hours of burning, the candlestick is 13.4 inches tall. Write and solve a linear equation to find the original height of the candle. Let h equal the number of hours the candlestick burns. We have a candlestick height equation of C. C = 13.4 + 0.2(8) <-- We need to add back the 8 hours of candlestick burning C = 13.4 + 1.6 C = [B]15 inches[/B]
A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will t
A car is purchased for $24,000 . Each year it loses 30% of its value. After how many years will the car be worth $7300 or less? (Use the calculator provided if necessary.) Write the smallest possible whole number answer. Set up the depreciation equation D(t) where t is the number of years in the life of the car: D(t) = 24,000/(1.3)^t The problem asks for D(t)<=7300 24,000/(1.3)^t = 7300 Cross multiply: 7300(1.3)^t = 24,000 Divide each side by 7300 1.3^t = 24000/7300 1.3^t = 3.2877 Take the natural log of both sides: LN(1.3^t) = LN(3.2877) Using the natural log identities, we have: t * LN(1.3) = 1.1902 t * 0.2624 = 1.1902 Divide each side by 0.2624 t = 4.5356 [B]Rounding this up, we have t = 5[/B]
A car is purchased for 27,000$. After each year the resale value decreases by 20%. What will the res
A car is purchased for 27,000$. After each year the resale value decreases by 20%. What will the resale value be after 3 years? If it decreases by 20%, it holds 100% - 20% = 80% of the value each year. So we have an equation R(t) where t is the time after purchase: R(t) = 27,000 * (0.8)^t The problem asks for R(3): R(3) = 27,000 * (0.8)^3 R(3) = 27,000 * 0.512 R(3) = [B]13.824[/B]
A car is traveling 60 km per hour. How many hours will it take for the car to reach a point that is
A car is traveling 60 km per hour. How many hours will it take for the car to reach a point that is 180 km away? Rate * Time = Distance so we have t for time as: 60t = 180 To solve this equation for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=60t%3D180&pl=Solve']type it in the search engine[/URL] and we get: t = [B]3[/B]
a car is worth 24000 and it depreciates 3000 a year how long till it costs 9000
a car is worth 24000 and it depreciates 3000 a year how long till it costs 9000 Let y be the number of years. We want to know y when: 24000 - 3000y = 9000 Typing [URL='https://www.mathcelebrity.com/1unk.php?num=24000-3000y%3D9000&pl=Solve']this equation into our search engine[/URL], we get: y = [B]5[/B]
a car was bought for $24300 and sold at a loss of $2290. Find the selling price.
a car was bought for $24300 and sold at a loss of $2290. Find the selling price. A loss means the car was sold for less than the buying price. Let the selling price be S. we have: 24300 - S = 2290 [URL='https://www.mathcelebrity.com/1unk.php?num=24300-s%3D2290&pl=Solve']Typing this equation into our search engine[/URL], we get: s = [B]22,010[/B]
A carpenter wants to cut a 45 inch board into two pieces such that the longer piece will be 7 inches
A carpenter wants to cut a 45 inch board into two pieces such that the longer piece will be 7 inches longer than the shorter. How long should each piece be Let the shorter piece of board length be s. Then the larger piece is: [LIST] [*]l = s + 7 [/LIST] And we know that: Shorter Piece + Longer Piece = 25 Substituting our values above, we have: s + s + 7 = 45 to solve this equation for s, we type it in our search engine and we get: s = [B]19[/B] Plugging this into our equation for l above means that: l = 19 + 7 l =[B] 26[/B]
A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge
A carpet cleaner charges $75 to clean the first 180 sq ft of carpet. There is an additional charge of 25� per square foot for any footage that exceeds 180 sq ft and $1.30 per step for any carpeting on a staircase. A customers cleaning bill was $253.95. This included the cleaning of a staircase with 14 steps. In addition to the staircase, how many square feet of carpet did the customer have cleaned? Calculate the cost of the staircase cleaning. Staircase cost = $1.30 * steps Staircase cost = $1.30 * 14 Staircase cost = $18.20 Subtract this from the cost of the total cleaning bill of $253.95. We do this to isolate the cost of the carpet. Carpet cost = $253.95 - $18.20 Carpet cost = $235.75 Now, the remaining carpet cost can be written as: 75 + $0.25(s - 180) = $235.75 <-- were s is the total square foot of carpet cleaned Multiply through and simplify: 75 + 0.25s - 45 = $235.75 Combine like terms: 0.25s + 30 = 235.75 [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B30%3D235.75&pl=Solve']Type this equation into our search engine[/URL] to solve for s, and we get: s = [B]823[/B]
A cash register contains $5 bills and $20 bills with a total value of $180 . If there are 15 bills t
A cash register contains $5 bills and $20 bills with a total value of $180 . If there are 15 bills total, then how many of each does the register contain? Let f be the number of $5 dollar bills and t be the number of $20 bills. We're given the following equations: [LIST=1] [*]f + t = 15 [*]5f + 20t = 180 [/LIST] We can solve this system of equations 3 ways. We get [B]t = 7[/B] and [B]f = 8[/B]. [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+15&term2=5f+%2B+20t+%3D+180&pl=Cramers+Method']Cramers Method[/URL] [/LIST]
A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How
A cashier has 44 bills, all of which are $10 or $20 bills. The total value of the money is $730. How many of each type of bill does the cashier have? Let a be the amount of $10 bills and b be the amount of $20 bills. We're given two equations: [LIST=1] [*]a + b = 44 [*]10a + 20b = 730 [/LIST] We rearrange equation 1 in terms of a. We subtract b from each side and we get: [LIST=1] [*]a = 44 - b [*]10a + 20b = 730 [/LIST] Now we substitute equation (1) for a into equation (2): 10(44 - b) + 20b = 730 Multiply through to remove the parentheses: 440 - 10b + 20b = 730 Group like terms: 440 + 10b = 730 Now, to solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=440%2B10b%3D730&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]29 [/B] To get a, we take b = 29 and substitute it into equation (1) above: a = 44 - 29 a = [B]15 [/B] So we have [B]15 ten-dollar bills[/B] and [B]29 twenty-dollar bills[/B]
A cashier has a total of 52 bills in her cash drawer. There are only $10 bills and $5 bills in her
A cashier has a total of 52 bills in her cash drawer. There are only $10 bills and $5 bills in her drawer. The value of the bills is $320. How many $10 bills are in the drawer? Let f be the amount of $5 bills in her drawer. Let t be the amount of $10 bills in her drawer. We're given two equations: [LIST=1] [*]f + t = 52 [*]5f + 10t = 320 [/LIST] We have a system of equations. We can solve this 3 ways below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+52&term2=5f+%2B+10t+%3D+320&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter what method we choose, we get: f = 40 and t = 12 So the answer for how many $10 bills are in the drawer is [B]12[/B]. Let's check our work for equation 1: 40 + 12 ? 52 52 = 52 <-- Confirmed Let's check our work for equation 2: 5(40) + 10(12) ? 320 200 + 120 ? 320 320 = 320 <-- Confirmed
A celebrity 50,000 followers on Instagram. The number of follower increases 45% each year. How many
A celebrity 50,000 followers on Instagram. The number of follower increases 45% each year. How many followers will they have after 8 years? We set up a growth equation for followers F(y), where y is the number of years passed since now: F(y) = 50000 * (1.45)^y <-- since 45% is 0.45 The problem asks for F(8): F(8) = 50000 * 1.45^8 F(8) = 50000 * 19.5408755063 F(8) = [B]977,044[/B]
A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m mi
A cell phone company charges a monthly rate of $12.95 and $0.25 a minute per call. The bill for m minutes is $21.20. Write an equation that models this situation. Let m be the number of minutes. We have the cost equation C(m): [B]0.25m + 12.95 = $21.20[/B]
A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 pe
A cell phone provider is offering an unlimited data plan for $70 per month or a 5 GB plan for $55 per month. However, if you go over your 5 GB of data in a month, you have to pay an extra $10 for each GB. How many GB would be used to make both plans cost the same? Let g be the number of GB. The limited plan has a cost as follows: C = 10(g - 5) + 55 C = 10g - 50 + 55 C = 10g + 5 We want to set the limited plan equal to the unlimited plan and solve for g: 10g + 5 = 70 Solve for [I]g[/I] in the equation 10g + 5 = 70 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 5 and 70. To do that, we subtract 5 from both sides 10g + 5 - 5 = 70 - 5 [SIZE=5][B]Step 2: Cancel 5 on the left side:[/B][/SIZE] 10g = 65 [SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE] 10g/10 = 65/10 g = [B]6.5[/B] Check our work for g = 6.5: 10(6.5) + 5 65 + 5 70
A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 p
A certain Illness is spreading at a rate of 10% per hour. How long will it take to spread to 1,200 people if 3 people initially exposes? Round to the nearest hour. Let h be the number of hours. We have the equation: 3 * (1.1)^h = 1,200 Divide each side by 3: 1.1^h = 400 [URL='https://www.mathcelebrity.com/natlog.php?num=1.1%5Eh%3D400&pl=Calculate']Type this equation into our search engine [/URL]to solve for h: h = 62.86 To the nearest hour, we round up and get [B]h = 63[/B]
A certain number added to its square is 30
Let x be the number. We have: x^2 + x = 30 Subtract 30 from each side: x^2 + x - 30 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-30%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get potential solutions of: [B]x = 5 or x = -6[/B] Check 5: 5 + 5^2 = 5 + 25 = [B]30[/B] Check -6 -6 + -6^2 = -6 + 36 = [B]30[/B]
A checking account is set up with an initial balance of $2400 and $200 are removed from the account
A checking account is set up with an initial balance of $2400 and $200 are removed from the account each month for rent right and equation who solution is the number of months and it takes for the account balance to reach 1000 200 is removed, so we subtract. Let m be the number of months. We want the following equation: [B]2400 - 200m = 1000 [/B] Now, we want to solve this equation for m. So [URL='https://www.mathcelebrity.com/1unk.php?num=2400-200m%3D1000&pl=Solve']we type it in our search engine[/URL] and we get: m = [B]7[/B]
A circle has a center at (6, 2) and passes through (9, 6)
A circle has a center at (6, 2) and passes through (9, 6) The radius (r) is found by [URL='https://www.mathcelebrity.com/slope.php?xone=6&yone=2&slope=+2%2F5&xtwo=9&ytwo=6&pl=You+entered+2+points']using the distance formula[/URL] to get: r = 5 And the equation of the circle is found by using the center (h, k) and radius r as: (x - h)^2 + (y - k)^2 = r^2 (x - 6)^2 + (y - 2)^2 = 5^2 [B](x - 6)^2 + (y - 2)^2 = 25[/B]
A class has 35 boys and girls. There are 7 more girls than boys. Find the number of girls and boys i
A class has 35 boys and girls. There are 7 more girls than boys. Find the number of girls and boys in the class Let the number of boys be b and the number of girls be g. We're given two equations: [LIST=1] [*]b + g = 35 [*]g = b + 7 (7 more girls means we add 7 to the boys) [/LIST] To solve for b, we substitute equation (2) into equation (1) for g: b + b + 7 = 35 To solve for b, we type this equation into our search engine and we get: b = [B]14[/B] Now, to solve for g, we plug b = 14 into equation (2) above: g = 14 + 7 g = [B]21[/B]
A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. En
A classroom fish tank contains x goldfish. The tank contains 4 times as many guppies as goldfish. Enter an equation that represents the total number of guppies, y, in the fish tank. The phrase [I]4 times as many[/I] means we multiply the goldfish (x) by 4 to get the number of guppies (y): [B]y = 4x[/B]
A classroom had x students. Then 9 of them went home. There are now 27 students in the classroom.
A classroom had x students. Then 9 of them went home. There are now 27 students in the classroom. Take this one piece at a time: [LIST] [*]We start with x students [*]9 of them went home. This means we have 9 less students. So we subtract 9 from x: x - 9 [*]The phrase [I]there are now[/I] means an equation, so we set x - 9 equal to 27 [/LIST] x - 9 = 27 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-9%3D27&pl=Solve']type it in our search engine[/URL] and we get: x = [B]36[/B]
a collection of 7 pencils, every week 3 more pencils are added How many weeks will it take to have 3
a collection of 7 pencils, every week 3 more pencils are added How many weeks will it take to have 30 pencils? Set up a function, P(w), where w is the number of weeks, and P(w) is the total amount of pencils after w weeks. We have: P(w) = 3w + 7 We want to know what w is when P(w) = 30 3w + 7 = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=3w%2B7%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get: w = 7.6667 We round up to the nearest integer, so we get [B]w = 8[/B]
A collection of nickels and dime has a total value of $8.50. How many coins are there if there are 3
A collection of nickels and dime has a total value of $8.50. How many coins are there if there are 3 times as many nickels as dimes. Let n be the number of nickels. Let d be the number of dimes. We're give two equations: [LIST=1] [*]n = 3d [*]0.1d + 0.05n = 8.50 [/LIST] Plug equation (1) into equation (2) for n: 0.1d + 0.05(3d) = 8.50 Multiply through: 0.1d + 0.15d = 8.50 [URL='https://www.mathcelebrity.com/1unk.php?num=0.1d%2B0.15d%3D8.50&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]d = 34[/B] Now, we take d = 34, and plug it back into equation (1) to solve for n: n = 3(34) [B]n = 102[/B]
A college student earns $21 per day delivering advertising brochures door-to-door, plus 50 cents for
A college student earns $21 per day delivering advertising brochures door-to-door, plus 50 cents for each person he interviews. How many people did he interview on a day when he earned $61.50 Let each person interviewed be p. We have an earnings equation E(p): E(p) = 0.5p + 21 The problems asks for p when E(p) = 61.50 0.5p + 21 = 61.50 To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.5p%2B21%3D61.50&pl=Solve']type this equation in our search engine[/URL] and we get: p = [B]81[/B]
A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number
A company charges $7 for a T-Shirt and ships and order for $22. A school principal ordered a number of T-shirts for the school store. The total cost of the order was $1,520. Which equation can be used to find the number one f shirts ordered? Set up the cost equation C(f) where f is the number of shirts: C(f) = Cost per shirt * f + Shipping We're given C(f) = 1520, Shipping = 22, and cost per shirt is 7, so we have: [B]7f + 22 = 1520 [/B] To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=7f%2B22%3D1520&pl=Solve']type this equation in our search engine[/URL] and we get: f = [B]214[/B]
A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How
A company has 3,100 employees and is expected to grow at a rate of 0.04 for the next six years. How many employees will they have in 6 years? Round to the nearest whole number. We build the following exponential equation: Final Balance = Initial Balance * (1 + growth rate)^time Final Balance = 3100(1.04)^6 Final Balance = 3100 * 1.2653190185 Final Balance = 3922.48895734 The problem asks us to round to the nearest whole number. Since 0.488 is less than 0.5, we round [U]down.[/U] Final Balance = [B]3,922[/B]
A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat.
A company makes toy boats. Their monthly fixed costs are $1500. The variable costs are $50 per boat. They sell boats for $75 a piece. How many boats must be sold each month to break even? [U]Set up Cost function C(b) where t is the number of tapestries:[/U] C(b) = Cost per boat * number of boats + Fixed Cost C(b) = 50b + 1500 [U]Set up Revenue function R(b) where t is the number of tapestries:[/U] R(b) = Sale Price * number of boats R(b) = 75b [U]Break even is where Revenue equals Cost, or Revenue minus Cost is 0, so we have:[/U] R(b) - C(b) = 0 75b - (50b + 1500) = 0 75b - 50b - 1500 = 0 25b - 1500 = 0 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-1500%3D0&pl=Solve']type this equation in our math engine[/URL] and we get: b = [B]60[/B]
A company specializes in personalized team uniforms. It costs the company $15 to make each uniform a
A company specializes in personalized team uniforms. It costs the company $15 to make each uniform along with their fixed costs at $640. The company plans to sell each uniform for $55. [U]The cost function for "u" uniforms C(u) is given by:[/U] C(u) = Cost per uniform * u + Fixed Costs [B]C(u) = 15u + 640[/B] Build the revenue function R(u) where u is the number of uniforms: R(u) = Sale Price per uniform * u [B]R(u) = 55u[/B] Calculate break even function: Break even is where Revenue equals cost C(u) = R(u) 15u + 640 = 55u To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=15u%2B640%3D55u&pl=Solve']type this equation into our search engine[/URL] and we get: u = [B]16 So we break even selling 16 uniforms[/B]
A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each l
A company that manufactures lamps has a fixed monthly cost of $1800. It costs $90 to produce each lamp, and the selling price is $150 per lamp. Set up the Cost Equation C(l) where l is the price of each lamp: C(l) = Variable Cost x l + Fixed Cost C(l) = 90l + 1800 Determine the revenue function R(l) R(l) = 150l Determine the profit function P(l) Profit = Revenue - Cost P(l) = 150l - (90l + 1800) P(l) = 150l - 90l - 1800 [B]P(l) = 60l - 1800[/B] Determine the break even point: Breakeven --> R(l) = C(l) 150l = 90l + 1800 [URL='https://www.mathcelebrity.com/1unk.php?num=150l%3D90l%2B1800&pl=Solve']Type this into the search engine[/URL], and we get [B]l = 30[/B]
A construction company can remove 2/3 tons of dirt from a construction site each hour. How long wil
A construction company can remove 2/3 tons of dirt from a construction site each hour. How long will it take them to remove 30 tons of dirt from the site? Let h be the number of hours. We have the following equation: 2/3h = 30 Multiply each side by 3: 2(3)h/3 = 30 * 3 Cancel the 3 on the left side: 2h = 90 [URL='https://www.mathcelebrity.com/1unk.php?num=2h%3D90&pl=Solve']Type 2h = 90 into the search engine[/URL], we get [B]h = 45[/B].
A construction crew has just built a new road. They built 43.75 kilometers of road at a rate of 7 ki
A construction crew has just built a new road. They built 43.75 kilometers of road at a rate of 7 kilometers per week. How many weeks did it take them? Let w = weeks 7 kilometers per week * w = 43.75 To solve for w, we divide each side of the equation by 7: 7w/7 = 43.75/7 Cancel the 7's, we get: w = [B]6.25 [/B]
A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8
A cookie recipe uses 10 times as much flour as sugar. If the total amount of these ingredients is 8 1/4 cups, how much flour and how much sugar would it be? Let f be the number of cups of sugar. And let f be the number of cups of flour. We're given two equations: [LIST=1] [*]f = 10s [*]s + f = 8 & 1/4 [/LIST] Substitute (1) into (2): s + 10s = 8 & 1/4 11fs= 33/4 <-- 8 & 1/4 = 33/4 Cross multiply: 44s = 33 Divide each side by 44: s= 33/44 Divide top and bottom by 11 and we get s [B]= 3/4 or 0.75[/B] Now substitute this into (1): f = 10(33/44) [B]f = 330/44 or 7 & 22/44 or 7.5[/B]
A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixe
A corn refining company produces corn gluten cattle feed at a variable cost of $84 per ton. If fixed costs are $110,000 per month and the feed sells for $132 per ton, how many tons should be sold each month to have a monthly profit of $560,000? [U]Set up the cost function C(t) where t is the number of tons of cattle feed:[/U] C(t) = Variable Cost * t + Fixed Costs C(t) = 84t + 110000 [U]Set up the revenue function R(t) where t is the number of tons of cattle feed:[/U] R(t) = Sale Price * t R(t) = 132t [U]Set up the profit function P(t) where t is the number of tons of cattle feed:[/U] P(t) = R(t) - C(t) P(t) = 132t - (84t + 110000) P(t) = 132t - 84t - 110000 P(t) = 48t - 110000 [U]The question asks for how many tons (t) need to be sold each month to have a monthly profit of 560,000. So we set P(t) = 560000:[/U] 48t - 110000 = 560000 [U]To solve for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=48t-110000%3D560000&pl=Solve']type this equation into our search engine[/URL] and we get:[/U] t =[B] 13,958.33 If the problem asks for whole numbers, we round up one ton to get 13,959[/B]
A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The tot
A crate contains 300 coins and stamps. The coins cost $3 each and the stamps cost $1.5 each. The total value of the items is $825. How many coins are there? Let c be the number of coins, and s be the number of stamps. We're given: [LIST=1] [*]c + s = 300 [*]3c + 1.5s = 825 [/LIST] We have a set of simultaneous equations, or a system of equations. We can solve this 3 ways: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+s+%3D+300&term2=3c+%2B+1.5s+%3D+825&pl=Cramers+Method']Cramers Method[/URL] [/LIST] No matter which way we pick, we get: s = 50 c = [B]250[/B]
A daily pass costs $62. A season ski pass costs $450. The skier would have to rent skis with eithe
A daily pass costs $62. A season ski pass costs $450. The skier would have to rent skis with either pass for $30 per day. How many days would the skier have to go skiing in order to make the season pass less expensive than the daily passes? Let d be the number of days the skier attends. Calculate the daily cost: Daily Total Cost = Daily Cost + Rental Cost Daily Total Cost = 62d + 30d Daily Total Cost = 92d Calculate Season Cost: Season Total Cost = Season Fee + Rental Cost Season Total Cost = 450 + 30d Set the daily total cost and season cost equal to each other: 450 + 30d = 92d [URL='https://www.mathcelebrity.com/1unk.php?num=450%2B30d%3D92d&pl=Solve']Typing this equation into the search engine[/URL], we get d = 7.258. We round up to the next full day of [B]8[/B]. Now check our work: Daily Total Cost for 8 days = 92(8) = 736 Season Cost for 8 days = 30(8) + 450 = 240 + 450 = 710. Therefore, the skier needs to go at least [B]8 days[/B] to make the season cost less than the daily cot.
A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog wa
A dog walker charges a flat rate of $6 per walk plus an hourly rate of $30. How much does the dog walker charge for a 3 hour walk? Set up the cost equation C(h) where h is the number of hours: C(h) = Hourly rate * h + flat rate C(h) = 30h + 6 The question asks for C(h) when h = 3: C(3) = 30(3) + 6 C(3) = 90 + 6 C(3) = [B]96[/B]
A dormitory manager buys 38 bed sheets and 61 towels for $791.50. The manager get another 54 bed she
A dormitory manager buys 38 bed sheets and 61 towels for $791.50. The manager get another 54 bed sheets and 50 towels for $923 from the same store. What is the cost of one bed sheet and one towel? Let s be bed sheets and t be towels. We have two equations: [LIST=1] [*]38s + 61t = 791.50 [*]54s + 50t = 923 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=38s+%2B+61t+%3D+791.50&term2=54s+%2B+50t+%3D+923&pl=Cramers+Method']system of equations calculator,[/URL] we get: [LIST] [*]s = 12 [*]t = 5.5 [/LIST]
A fair charges an admission fee of 4 dollars for each person. Let C be the cost of admission (in d
A fair charges an admission fee of 4 dollars for each person. Let C be the cost of admission (in dollars) for P people. Write an equation relating C to P. [B]C = 4P[/B]
A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with
A family buys airline tickets online. Each ticket costs $167. The family buys travel insurance with each ticket that costs $19 per ticket. The Web site charges a fee of $16 for the entire purchase. The family is charged a total of $1132. How many tickets did the family buy? Let t be the number of tickets. We have the following equation with ticket price, insurance, and flat fee: 167t + 19t + 16 = 1132 Combine like terms: 186t + 16 = 1132 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=186t%2B16%3D1132&pl=Solve']equation calculator[/URL], we have: [B]t = 6[/B]
A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at
A farmer bought a number of pigs for $232. However, 5 of them died before he could sell the rest at a profit of 4 per pig. His total profit was $56. How many pigs did he originally buy? Let p be the purchase price of pigs. We're given: [LIST] [*]Farmer originally bought [I]p [/I]pigs for 232 which is our cost C. [*]5 of them died, so he has p - 5 left [*]He sells 4(p - 5) pigs for a revenue amount R [*]Since profit is Revenue - Cost, which equals 56, we have: [/LIST] Calculate Profit P = R - C Plug in our numbers: 4(p - 5) - 232 = 56 4p - 20 - 232 = 56 To solve for p, [URL='https://www.mathcelebrity.com/1unk.php?num=4p-20-232%3D56&pl=Solve']we type this equation into our search engine[/URL] and we get: p = [B]77[/B]
A farmer sold 250 of his sheep, bought 35 and then bought 68. If he now has 190, how many did he beg
A farmer sold 250 of his sheep, bought 35 and then bought 68. If he now has 190, how many did he begin with? Let's start his count with x. We have: x - 250 + 35 + 68 = 190 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=x-250%2B35%2B68%3D190&pl=Solve']equation solver[/URL], we get x = [B]337[/B]
A first number plus twice a second number is 10. Twice the first number plus the second totals 29. F
A first number plus twice a second number is 10. Twice the first number plus the second totals 29. Find the numbers. Let the first number be x. Let the second number be y. We are given the following two equations: [LIST=1] [*]x + 2y = 10 [*]2x + y = 29 [/LIST] We can solve this 3 ways using: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Substitution']Substitution[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Elimination']Elimination[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+10&term2=2x+%2By+%3D+29&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] Using any of the 3 methods, we get the same answers of [B](x, y) = (16, -3)[/B]
A first number plus twice a second number is 10. Twice the first number plus the second totals 35. F
A first number plus twice a second number is 10. Twice the first number plus the second totals 35. Find the numbers. [U]The phrase [I]a number[/I] means an arbitrary variable[/U] A first number is written as x A second number is written as y [U]Twice a second number means we multiply y by 2:[/U] 2y [U]A first number plus twice a second number:[/U] x + 2y [U]A first number plus twice a second number is 10 means we set x + 2y equal to 10:[/U] x + 2y = 10 [U]Twice the first number means we multiply x by 2:[/U] 2x [U]Twice the first number plus the second:[/U] 2x + y [U]Twice the first number plus the second totals 35 means we set 2x + y equal to 35:[/U] 2x + y = 35 Therefore, we have a system of two equations: [LIST=1] [*]x + 2y = 10 [*]2x + y = 35 [/LIST] Since we have an easy multiple of 2 for the x variable, we can solve this by multiply the first equation by -2: [LIST=1] [*]-2x - 4y = -20 [*]2x + y = 35 [/LIST] Because the x variables are opposites, we can add both equations together: (-2 + 2)x + (-4 + 1)y = -20 + 35 The x terms cancel, so we have: -3y = 15 To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D15&pl=Solve']type it in our search engine[/URL] and we get: y = [B]-5 [/B] Now we substitute this y = -5 into equation 2: 2x - 5 = 35 To solve this equation for x, we[URL='https://www.mathcelebrity.com/1unk.php?num=2x-5%3D35&pl=Solve'] type it in our search engine[/URL] and we get: x = [B]20[/B]
A first number plus twice a second number is 11. Twice the first number plus the second totals 34. F
A first number plus twice a second number is 11. Twice the first number plus the second totals 34. Find the numbers. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x + 2y = 11 [*]2x + y = 34 [/LIST] Using our simultaneous equations calculator, we have 3 methods to solve this: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+11&term2=2x+%2B+y+%3D+34&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] All 3 methods give the same solution: [LIST] [*][B]x = 19[/B] [*][B]y = -4[/B] [/LIST]
A first number plus twice a second number is 14. Twice the first number plus the second totals 40. F
A first number plus twice a second number is 14. Twice the first number plus the second totals 40. Find the numbers. [B][U]Givens and assumptions:[/U][/B] [LIST] [*]Let the first number be x. [*]Let the second number be y. [*]Twice means multiply by 2 [*]The phrases [I]is[/I] and [I]totals[/I] mean equal to [/LIST] We're given two equations: [LIST=1] [*]x + 2y = 14 [*]2x + y = 40 [/LIST] To solve this system, we can take a shortcut, and multiply the top equation by -2 to get our new system: [LIST=1] [*]-2x - 4y = -28 [*]2x + y = 40 [/LIST] Now add both equations together (-2 _ 2)x (-4 + 1)y = -28 + 40 -3y = 12 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=-3y%3D12&pl=Solve']type it in our search engine[/URL] and we get: y = [B]-4 [/B] We substitute this back into equation 1 for y = -4: x + 2(-4) = 14 x - 8 = 14 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-8%3D14&pl=Solve']type it in our search engine[/URL] and we get: x = [B]22[/B]
A first number plus twice a second number is 22. Twice the first number plus the second totals 28. F
A first number plus twice a second number is 22. Twice the first number plus the second totals 28. Find the numbers. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x + 2y = 22 <-- Since twice means multiply by 2 [*]2x + y = 28 <-- Since twice means multiply by 2 [/LIST] We have a set of simultaneous equations. We can solve this three ways [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28+&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+22&term2=2x+%2B+y+%3D+28&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter which method we use, we get the same answer: [LIST] [*][B]x = 11 & 1/3[/B] [*][B]y = 5 & 1/3[/B] [/LIST]
A first number plus twice a second number is 3. Twice the first number plus the second totals 24.
A first number plus twice a second number is 3. Twice the first number plus the second totals 24. Let the first number be x. Let the second number be y. We're given: [LIST=1] [*]x + 2y = 3 <-- Because [I]twice[/I] means multiply by 2 [*]2x + y = 24 <-- Because [I]twice[/I] means multiply by 2 [/LIST] We have a system of equations. We can solve it any one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+2y+%3D+3&term2=2x+%2B+y+%3D+24&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which way we choose, we get: [LIST] [*]x = [B]15[/B] [*]y = [B]-6[/B] [/LIST]
A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Fi
A first number plus twice a second number is 6. Twice the first number plus the second totals 15. Find the numbers. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x + 2y = 6 [*]2x + y = 15 [/LIST] Multiply the first equation by -2: [LIST=1] [*]-2x - 4y = -12 [*]2x + y = 15 [/LIST] Now add them -2x + 2x - 4y + y = -12 + 15 -3y = 3 Divide each side by -3: y = 3/-3 y =[B] -1[/B] Plug this back into equation 1: x + 2(-1) = 6 x - 2 = 6 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x-2%3D6&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]8[/B]
A first number plus twice a second number is 7
A first number plus twice a second number is 7 Let the first number be x. Let the second number be y. We're given: [LIST] [*]A first number is x [*]A second number is y [*]Twice the second number means we multiply y by 2: 2y [*][I]Plus [/I]means we add x to 2y: x + 2y [*]The phrase [I]is[/I] means an equation, so we set x + 2y equal to 7 [/LIST] [B]x + 2y = 7[/B]
A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will
A flower bed is to be 3 m longer than it is wide. The flower bed will an area of 108 m2 . What will its dimensions be? A flower bed has a rectangle shape, so the area is: A = lw We are given l = w + 3 Plugging in our numbers given to us, we have: 108 = w(w + 3) w^2 + 3w = 108 Subtract 108 from each side: w^2 + 3w - 108 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B3w-108%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get: w = (9, -12) Since length cannot be negative, w = 9. And l = 9 + 3 --> l = 12 So we have [B](l, w) = (12, 9)[/B] Checking our work, we have: A = (12)9 A = 108 <-- Match!
A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from sel
A food truck sells salads for $6.50 each and drinks for $2.00 each. The food trucks revenue from selling a total of 209 salads and drinks in one day was $836.50. How many salads were sold that day? Let the number of drinks be d. Let the number of salads be s. We're given two equations: [LIST=1] [*]2d + 6.50s = 836.50 [*]d + s = 209 [/LIST] We can use substitution to solve this system of equations quickly. The question asks for the number of salads (s). Therefore, we want all expressions in terms of s. Rearrange Equation 2 by subtracting s from both sides: d + s - s = 209 - s Cancel the s's, we get: d = 209 - s So we have the following system of equations: [LIST=1] [*]2d + 6.50s = 836.50 [*]d = 209 - s [/LIST] Substitute equation (2) into equation (1) for d: 2(209 - s) + 6.50s = 836.50 Multiply through to remove the parentheses: 418 - 2s + 6.50s = 836.50 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=418-2s%2B6.50s%3D836.50&pl=Solve']type it into our search engine and we get[/URL]: s = [B]93[/B]
A football gained 52 yards during the possession. In the next 3 possessions they gained the same amo
A football gained 52 yards during the possession. In the next 3 possessions they gained the same amount of yards each time. If they gained a total of 256 yards, write and solve an equation for how many yards they gained in each of the last 3 possessions. Subtract 52 initial yards 256 - 52 = 204 Now, divide 204 by 3 possessions 204/3 = [B]68 yards[/B]
a football team won 3 more games than it lost.the team played 11 games.how many did it win?
a football team won 3 more games than it lost.the team played 11 games.how many did it win? Let wins be w. Let losses be l. We're given two equations: [LIST=1] [*]w = l + 3 [*]l + w = 11 [/LIST] Plug equation (1) into equation (2) to solve for l: l + (l + 3) = 11 Group like terms: 2l + 3 = 11 [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B3%3D11&pl=Solve']Typing this equation into our search engine[/URL], we get: l = 4 To solve for w, we plug in l = 4 above into equation (1): w = 4 + 3 w = [B]7[/B]
A garden table and a bench cost $977 combined. The garden
A garden table and a bench cost $977 combined. The garden table costs $77 more than the bench. What is the cost of the bench? Let the garden table cost be g and the bench cost be b. We're given [LIST=1] [*]b + g = 977 [*]g = b + 77 <-- The phrase [I]more than[/I] means we add [/LIST] Substitute (2) into (1): b + (b + 77) = 977 Combine like terms: 2b + 77 = 977 [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B77%3D977&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]b = $450[/B]
A girl is three years older than her brother. If their combined age is 35 years, how old is each
A girl is three years older than her brother. If their combined age is 35 years, how old is each Let the girl's age be g. Let the boy's age be b. We're given two equations: [LIST=1] [*]g = b + 3 ([I]Older means we add)[/I] [*]b + g = 35 [/LIST] Now plug in equation (1) into equation (2) for g: b + b + 3 = 35 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2Bb%2B3%3D35&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]16 [/B] Now, to solve for g, we plug in b = 16 that we just solved for into equation (1): g = 16 + 3 g = [B]19[/B]
A group of campers have 250 pounds of food. They plan to eat 12 pounds a day. How many days will it
A group of campers have 250 pounds of food. They plan to eat 12 pounds a day. How many days will it take them to eat the food. Write your answer in a linear equation. Let the number of days be d. We have the following equation: 12d = 250 To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=12d%3D250&pl=Solve']type this equation in our search engine[/URL] and we get: d = [B]20.833[/B]
A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A star
A group of scientists studied the effect of a chemical on various strains of bacteria. Strain A started with 6000 cells and decreased at a constant rate of 2000 cells per hour after the chemical was applied. Strain B started with 2000 cells and decreased at a constant rate of 1000 cells per hour after the chemical was applied. When will the strains have the same number of cells? Explain. Set up strain equations where h is the number of hours since time 0: [LIST] [*]Strain A: 6000 - 2000h [*]Strain B: 2000 - 1000h [/LIST] Set them equal to each other 6000 - 2000h = 2000 - 1000h Using our [URL='http://www.mathcelebrity.com/1unk.php?num=6000-2000h%3D2000-1000h&pl=Solve']equation solver[/URL], we see that [B]h = 4[/B]
A gym has yoga classes. Each class has 11 students. If there are c classes, write an equation to rep
A gym has yoga classes. Each class has 11 students. If there are c classes, write an equation to represent the total number of students s taking yoga. Total students is the number of classes times the number of students in each class: [B]s = 11c[/B]
A gym has yoga classes. Each class has 14 students. If there are c classes write an equation to repr
A gym has yoga classes. Each class has 14 students. If there are c classes write an equation to represent the total number of students s taking yoga s = students per class * number of classes [B]s = 14c[/B]
A gym membership has a $50 joining fee plus charges $17 a month for m months
A gym membership has a $50 joining fee plus charges $17 a month for m months Build a cost equation C(m) where m is the number of months of membership. C(m) = Variable Cost * variable units + Fixed Cost C(m) = Months of membership * m + Joining Fee Plugging in our numbers and we get: [B]C(m) = 17m + 50 [MEDIA=youtube]VGXeqd3ikAI[/MEDIA][/B]
A high school graduating class is made up of 440 students. There are 168 more girls than boys. How m
A high school graduating class is made up of 440 students. There are 168 more girls than boys. How many boys are in the class? Let b be the number of boys and g be the number of girls. We're given 2 equations: [LIST=1] [*]b + g = 440 [*]g = b + 168 [/LIST] Substitute (2) into (1) b + (b + 168) = 440 Combine like terms: 2b + 168 = 440 [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B168%3D440&pl=Solve']Type this equation into the search engine[/URL], and we get: [B]b = 136[/B]
A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 2
A home is to be built on a rectangular plot of land with a perimeter of 800 feet. If the length is 20 feet less than 3 times the width, what are the dimensions of the rectangular plot? [U]Set up equations:[/U] (1) 2l + 2w = 800 (2) l = 3w - 20 [U]Substitute (2) into (1)[/U] 2(3w - 20) + 2w = 800 6w - 40 + 2w = 800 [U]Group the w terms[/U] 8w - 40 = 800 [U]Add 40 to each side[/U] 8w = 840 [U]Divide each side by 8[/U] [B]w = 105 [/B] [U]Substitute w = 105 into (2)[/U] l = 3(105) - 20 l = 315 - 20 [B]l = 295[/B]
a horse and a saddle cost $5,000. if the horse cost 4 times as much as the saddle, what was the cost
a horse and a saddle cost $5,000. if the horse cost 4 times as much as the saddle, what was the cost of each? Let the cost of the horse be h, and the cost of the saddle be s. We're given: [LIST=1] [*]h + s = 5000 [*]h = 4s [/LIST] Substitute equation (2) into equation (1): 4s + s = 5000 [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2Bs%3D5000&pl=Solve']Type this equation into the search engine[/URL], we get: [B]s = 1,000[/B] Substitute s = 1000 into equation (2): h = 4(1000) [B]h = 4,000[/B]
A house costs 3.5 times as much as the lot. Together they sold for $135,000. Find the cost of each
A house costs 3.5 times as much as the lot. Together they sold for $135,000. Find the cost of each. Let the house cost be h, and the lot cost be l. We have the following equations: [LIST=1] [*]h = 3.5l [*]h + l = 135,000 [/LIST] Substitute (1) into (2) 3.5l + l = 135,000 Combine like terms: 4.5l = 135,000 Divide each side by 4.5 to isolate l [B]l = 30,000[/B] Substitute this back into equation (1) h = 3.5(30,000) [B]h = 105,000[/B]
A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus
A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which companies will charge the same amount? Set up the cost function C(h) where h is the number of hours. Company 1: C(h) = 12h + 376 Company 2: C(h) = 15h + 280 To see when the companies charge the same amount, set both C(h) functions equal to each other. 12h + 376 = 15h + 280 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B376%3D15h%2B280&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]32[/B]
A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus
A house painting company charges $376 plus $12 per hour. Another painting company charges $280 plus $15 per hour. How long is a job for which both companies will charge the same amount? [U]Set up the cost function for the first company C(h) where h is the number of hours:[/U] C(h) = Hourly Rate * h + flat rate C(h) = 12h + 376 [U]Set up the cost function for the first company C(h) where h is the number of hours:[/U] C(h) = Hourly Rate * h + flat rate C(h) = 15h + 280 The problem asks how many hours will it take for both companies to charge the same. So we set the cost functions equal to each other: 12h + 376 = 15h + 280 Plugging this equation [URL='https://www.mathcelebrity.com/1unk.php?num=12h%2B376%3D15h%2B280&pl=Solve']into our search engine and solving for h[/URL], we get: h = [B]32[/B]
a is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how o
a is 2 years older than b who is twice as old as c. if the total ages of a,b and c is 42, then how old is b We're given 3 equations: [LIST=1] [*]a = b + 2 [*]b = 2c [*]a + b + c = 42 [/LIST] Substituting equation (2) into equation (1), we have: a = 2c + 2 Since b = 2c, we substitute both of these into equation (3) to get: 2c + 2 + 2c + c = 42 To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=2c%2B2%2B2c%2Bc%3D42&pl=Solve']type this equation into our math engine[/URL] and we get: c = 8 Now take c = 8 and substitute it into equation (2) above: b = 2(8) b = [B]16[/B]
A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hour
A jet plane traveling at 550 mph over takes a propeller plane traveling at 150 mph that had a 3 hours head start. How far from the starting point are the planes? Use the formula D = rt where [LIST] [*]D = distance [*]r = rate [*]t = time [/LIST] The plan traveling 150 mph for 3 hours: Time 1 = 150 Time 2 = 300 Time 3 = 450 Now at Time 3, the other plane starts Time 4 = 600 Time 5 = 750 Time 6 = 450 + 150t = 550t Subtract 150t 400t = 450 Divide each side by 400 t = 1.125 Plug this into either distance equation, and we get: 550(1.125) = [B]618.75 miles[/B]
A jet travels at 485 miles per hour. Which equation represents the distance, d, that the jet will tr
A jet travels at 485 miles per hour. Which equation represents the distance, d, that the jet will travel in t hours. The distance formula is: d = rt We're given r = 485, so we have: [B]d = 485t[/B]
A kilogram of chocolate costs8 dollars. Sally buys p kilograms. Write an equation to represent the t
A kilogram of chocolate costs8 dollars. Sally buys p kilograms. Write an equation to represent the total cost c that Sally pays. c[B] = 8p[/B]
a large fry has 120 more calories than a small. 5 large fries is the same amount of calories as 7 sm
a large fry has 120 more calories than a small. 5 large fries is the same amount of calories as 7 small. How many calories does each size fry have? Let the number of calories in large fries be l. Let the number of calories in small fries be s. We're given two equations: [LIST=1] [*]l = s + 120 [*]5l = 7s [/LIST] Substitute equation (1) into equation (2): 5(s + 120) = 7s [URL='https://www.mathcelebrity.com/1unk.php?num=5%28s%2B120%29%3D7s&pl=Solve']Type this equation into the search engine[/URL] and we get: s = [B]300[/B] Substitute s = 300 into equation (1): l = 300 + 120 l = [B]420[/B]
A line has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form
A line has a slope of 7 and a y-intercept of -4. What is its equation in slope intercept form The slope-intercept equation for a line: y = mx + b where m is the slope Given m = 7, we have: y = 7x + b The y-intercept is found by setting x to 0: y = 7(0) + b y = 0 + b y = b We're given the y-intercept is -4, so we have: b = -4 So our slope-intercept equation is: [B]y = 7x - 4[/B]
A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that lin
A line in the xy-plane passes through the origin and has a slope of 4/5. What points lie on that line. Our line equation is: y = mx + b We're given: m = 4/5 (x, y) = (0, 0) So we have: 0 = 4/5(0) + b 0 = 0 + b b = 0 Therefore, our line equation is: y = 4/5x [URL='https://www.mathcelebrity.com/function-calculator.php?num=y%3D4%2F5x&pl=Calculate']Start plugging in values here to get a list of points[/URL]
A line passes through the point -3,4 and has a slope of -5
A line passes through the point -3,4 and has a slope of -5 Using our [URL='http://A line passes through the point -3,4 and has a slope of -5']point slope calculator[/URL], we get a line equation of: y = -5x - 11
A local Dunkin� Donuts shop reported that its sales have increased exactly 16% per year for the last
A local Dunkin� Donuts shop reported that its sales have increased exactly 16% per year for the last 2 years. This year�s sales were $80,642. What were Dunkin' Donuts' sales 2 years ago? Declare variable and convert numbers: [LIST] [*]16% = 0.16 [*]let the sales 2 years ago be s. [/LIST] s(1 + 0.16)(1 + 0.16) = 80,642 s(1.16)(1.16) = 80,642 1.3456s = 80642 Solve for [I]s[/I] in the equation 1.3456s = 80642 [SIZE=5][B]Step 1: Divide each side of the equation by 1.3456[/B][/SIZE] 1.3456s/1.3456 = 80642/1.3456 s = 59930.142687277 s = [B]59,930.14[/B]
A local shop sold 499 hamburgers and cheese burgers. There were 51 fewer cheese burgers sold. How ma
A local shop sold 499 hamburgers and cheese burgers. There were 51 fewer cheese burgers sold. How many hamburgers were sold? Let h = number of hamburgers sold and c be the number of cheeseburgers sold. We have two equations: (1) c = h - 51 (2) c + h = 499 Substitute (1) into (2) h - 51 + h = 499 Combine like terms 2h - 51 = 499 Add 51 to both sides 2h = 550 Divide each side by 2 to isolate h [B]h = 275[/B]
A machine prints 230 movie posters each hour. Write and solve an equation to find the number of hour
A machine prints 230 movie posters each hour. Write and solve an equation to find the number of hours it takes the machine to print 1265 posters. Let h be the number of hours. We're given the following expression for the printing output of the machine: 230h The questions asks for how long (h) to print 1265 posters, so we setup the equation: 230h = 1265 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=230h%3D1265&pl=Solve']type this equation into our math engine[/URL] and we get: h = [B]5.5 hours[/B]
A machine shop employee earned $642 last week. She worked 40hours at her regular rate and 9 hours at
A machine shop employee earned $642 last week. She worked 40hours at her regular rate and 9 hours at a time and a half rate. Find her regular hourly rate. Let the regular hourly rate be h. We're given: 40h + 40(1.5)(h - 40) = 642 Multiply through and simplify: 40h + 60h - 2400 = 642 100h - 2400 = 642 [URL='https://www.mathcelebrity.com/1unk.php?num=100h-2400%3D642&pl=Solve']To solve for h, we type this equation into our search engine[/URL] and we get: h = [B]30.42[/B]
A mail courier charges a base fee of $4.95 plus $11.90 per package being delivered. If x represents
A mail courier charges a base fee of $4.95 plus $11.90 per package being delivered. If x represents the number of packages delivered, which of the following equations could be used to find y, the total cost of mailing packages? Set up the cost function y = C(x) [B]C(x) = 4.95 + 11.90x[/B]
A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add the
A man is 5 years older than his wife, and the daughter age is half of the mother, and if you add their ages is equal 100 Let the man's age be m. Let the wife's age be w. Let the daughter's age be d. We're given: [LIST=1] [*]m = w + 5 [*]d = 0.5m [*]d + m + w = 100 [/LIST] Rearrange equation 1 in terms of w my subtracting 5 from each side: [LIST=1] [*]w = m - 5 [*]d = 0.5m [*]d + m + w = 100 [/LIST] Substitute equation (1) and equation (2) into equation (3) 0.5m + m + m - 5 = 100 We [URL='https://www.mathcelebrity.com/1unk.php?num=0.5m%2Bm%2Bm-5%3D100&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get: m = [B]42 [/B] Now, substitute m = 42 into equation 2 to solve for d: d = 0.5(42) d = [B]21 [/B] Now substitute m = 42 into equation 1 to solve for w: w = 42 - 5 w = [B]37 [/B] To summarize our ages: [LIST] [*]Man (m) = 42 years old [*]Daughter (d) = 21 years old [*]Wife (w) = 37 years old [/LIST]
A man is four time as old as his son. How old is the man if the sum of their ages is 60?
A man is four time as old as his son. How old is the man if the sum of their ages is 60? Let the son's age be a. Then the man's age is 4a. If the sum of their ages is 60, we have: a + 4a = 60 To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B4a%3D60&pl=Solve']type it in our math engine[/URL] and we get: a = 12 Therefore, the man's age is: 4(12) = [B]48[/B]
A man is four times as old as his son. In five years time he will be three times as old. Find their
A man is four times as old as his son. In five years time he will be three times as old. Find their present ages. Let the man's age be m, and the son's age be s. We have: [LIST=1] [*]m = 4s [*]m + 5 = 3(s + 5) [/LIST] Substitute (1) into (2) 4s + 5 = 3s + 15 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=4s%2B5%3D3s%2B15&pl=Solve']equation calculator[/URL], and we get [B]s = 10[/B]. m = 4(10) [B]m = 40[/B]
A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children
A man purchased 20 tickets for a total of $225. The tickets cost $15 for adults and $10 for children. What was the cost of each ticket? Declare variables: [LIST] [*]Let a be the number of adult's tickets [*]Let c be the number of children's tickets [/LIST] Cost = Price * Quantity We're given two equations: [LIST=1] [*]a + c = 20 [*]15a + 10c = 225 [/LIST] Rearrange equation (1) in terms of a: [LIST=1] [*]a = 20 - c [*]15a + 10c = 225 [/LIST] Now that I have equation (1) in terms of a, we can substitute into equation (2) for a: 15(20 - c) + 10c = 225 Solve for [I]c[/I] in the equation 15(20 - c) + 10c = 225 We first need to simplify the expression removing parentheses Simplify 15(20 - c): Distribute the 15 to each term in (20-c) 15 * 20 = (15 * 20) = 300 15 * -c = (15 * -1)c = -15c Our Total expanded term is 300-15c Our updated term to work with is 300 - 15c + 10c = 225 We first need to simplify the expression removing parentheses Our updated term to work with is 300 - 15c + 10c = 225 [SIZE=5][B]Step 1: Group the c terms on the left hand side:[/B][/SIZE] (-15 + 10)c = -5c [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] -5c + 300 = + 225 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 300 and 225. To do that, we subtract 300 from both sides -5c + 300 - 300 = 225 - 300 [SIZE=5][B]Step 4: Cancel 300 on the left side:[/B][/SIZE] -5c = -75 [SIZE=5][B]Step 5: Divide each side of the equation by -5[/B][/SIZE] -5c/-5 = -75/-5 c = [B]15[/B] Recall from equation (1) that a = 20 - c. So we substitute c = 15 into this equation to solve for a: a = 20 - 15 a = [B]5[/B]
A man's age (a) 10 years ago is 43
A man's age (a) 10 years ago is 43 [U]10 years ago means we subtract 10 from a:[/U] a - 10 [U]The word [I]is[/I] means an equation. So we set a - 10 equal to 43 to get our algebraic expression[/U] [B]a - 10 = 43[/B] If the problem asks you to solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=a-10%3D43&pl=Solve']we type this equation into our search engine[/URL] and we get: a = 53
A man's age (a) 10 years ago is 43.
A man's age (a) 10 years ago is 43. Years ago means we subtract [B]a - 10 = 43 [/B] If the problem asks you to solve for a, we type this equation into our math engine and we get: Solve for [I]a[/I] in the equation a - 10 = 43 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 43. To do that, we add 10 to both sides a - 10 + 10 = 43 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] a = [B]53[/B]
A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produ
A manufacturer has a monthly fixed cost of $100,000 and a production cost of $10 for each unit produced. The product sells for $22/unit. The cost function for each unit u is: C(u) = Variable Cost * Units + Fixed Cost C(u) = 10u + 100000 The revenue function R(u) is: R(u) = 22u We want the break-even point, which is where: C(u) = R(u) 10u + 100000 = 22u [URL='https://www.mathcelebrity.com/1unk.php?num=10u%2B100000%3D22u&pl=Solve']Typing this equation into our search engine[/URL], we get: u =[B]8333.33[/B]
A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produ
A manufacturer has a monthly fixed cost of $100,000 and a production cost of $12 for each unit produced. The product sells for $20/unit [U]Cost Function C(u) where u is the number of units:[/U] C(u) = cost per unit * u + fixed cost C(u) = 12u + 100000 [U]Revenue Function R(u) where u is the number of units:[/U] R(u) = Sale price * u R(u) = 20u Break even point is where C(u) = R(u): C(u) = R(u) 12u + 100000 = 20u To solve for u, we [URL='https://www.mathcelebrity.com/1unk.php?num=12u%2B100000%3D20u&pl=Solve']type this equation into our search engine[/URL] and we get: u = [B]12,500[/B]
A manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produce
A manufacturer has a monthly fixed cost of $25,500 and a production cost of $7 for each unit produced. The product sells for $10/unit. Set up cost function where u equals each unit produced: C(u) = 7u + 25,500 Set up revenue function R(u) = 10u Break Even is where Cost equals Revenue 7u + 25,500 = 10u Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=7u%2B25500%3D10u&pl=Solve']equation calculator[/URL] to get [B]u = 8,500[/B]
A math teacher bought 40 calculators at $8.20 each and a number of other calculators costing$2.95 ea
A math teacher bought 40 calculators at $8.20 each and a number of other calculators costing$2.95 each. In all she spent $387. How many of the cheaper calculators did she buy Let the number of cheaters calculators be c. Since amount equals price * quantity, we're given the following equation: 8.20 * 40 + 2.95c = 387 To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=8.20%2A40%2B2.95c%3D387&pl=Solve']type it in our search engine [/URL]and we get: c = [B]20[/B]
A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 poin
A math test is worth 100 points and has 38 problems. Each problem is worth either 5 points or 2 points. How many problems of each point value are on the test? Let's call the 5 point questions m for multiple choice. Let's call the 2 point questions t for true-false. We have two equations: [LIST=1] [*]m + t = 38 [*]5m + 2t = 100 [/LIST] Rearrange (1) to solve for m - subtract t from each side: 3. m = 38 - t Now, substitute (3) into (2) 5(38 - t) + 2t = 100 190 - 5t + 2t = 100 Combine like terms: 190 - 3t = 100 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=190-3t%3D100&pl=Solve']equation solver[/URL], we get [B]t = 30[/B]. Plugging t = 30 into (1), we get: 30 + t = 38 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=m%2B30%3D38&pl=Solve']equation solver[/URL] again, we get [B]m = 8[/B]. Check our work for (1) 8 + 30 = 38 <-- Check Check our work for (2) 5(8) + 2(30) ? 100 40 + 60 ? 100 100 = 100 <-- Check You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+38&term2=5m+%2B+2t+%3D+100&pl=Cramers+Method']simultaneous equations calculator[/URL]
A mechanic charges $50 to inspect your heater, plus $80 per hour to work on it. You owe the mechani
A mechanic charges $50 to inspect your heater, plus $80 per hour to work on it. You owe the mechanic a total of $310. Write and solve an equation to find the amount of time h (in hours) the mechanic works on your heater. We calculate the cost function C(h) as: C(h) = Hourly Rate * hours + Flat Fee Inspection C(h) = 80h + 50 <-- this is our cost equation Now, we want to solve for h when C(h) = 310 80h + 50 = 310 [URL='https://www.mathcelebrity.com/1unk.php?num=80h%2B50%3D310&pl=Solve']We type this equation into our search engine[/URL] and we get: h = [B]3.25[/B]
A mechanic will charge a new customer $45.00 for an initial diagnosis plus $20 an hour of labor. How
A mechanic will charge a new customer $45.00 for an initial diagnosis plus $20 an hour of labor. How long did the mechanic work on a car if he charged the customer $165? We set up a cost function C(h) where h is the number of hours of labor: C(h) = Hourly Labor Rate * h + Initial Diagnosis C(h) = 20h + 45 The problem asks for the number of hours if C(h) = 165. So we set our cost function C(h) above equal to 165: 20h + 45 = 165 To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B45%3D165&pl=Solve']we plug this equation into our search engine[/URL] and we get: h = [B]6[/B]
A medium orange has 70 calories. This is 10 calories less then 1/4 of the calories in a sugar krunch
A medium orange has 70 calories. This is 10 calories less then 1/4 of the calories in a sugar krunchy. How many calories are in a sugar crunchy? Let s = calories in a sugar crunch. Let o = 70 be the calories in a medium orange. Set up the equation: o = 1/4s - 10 70 = 1/4s - 10 Add 10 to each side 1/4s = 80 Multiply each side by 4 [B]s = 320[/B]
A monster energy drink has 164 mg of caffeine. Each hour your system reduces the amount of caffeine
A monster energy drink has 164 mg of caffeine. Each hour your system reduces the amount of caffeine by 12%. Write an equation that models the amount of caffeine that remains in your body after you drink an entire monster energy. Set up a function C(h) where he is the number of hours after you drink the Monster energy drink: Since 12% as a decimal is 0.12, we have: C(h) = 164 * (1 - 0.12)^h <-- we subtract 12% since your body flushes it out [B]C(h) = 164 * (0.88)^h[/B]
A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age o
A mother gives birth to a 10 pound baby. Every 2 months, the baby gains 5 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight. If the baby gains 5 pounds every 2 months, then they gain 5/2 = 2.5 pounds per month. Let x be the number of months old for the baby, we have: The baby starts at 10 pounds. And every month (x), the baby's weight increases 2.5 pounds. Our equation is: [B]y = 2.5x + 10[/B]
A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of
A mother gives birth to a 6 pound baby. Every 4 months, the baby gains 4 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx b that describes the baby's weight. The baby gains 4 pounds every month, where x is the number of months since birth. The baby boy starts life (time 0) at 6 pounds. So we have [B]y = 4x + 6[/B]
A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of
A mother gives birth to a 7 pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y = mx + b that describes the baby's weight. Every month, the baby gains 2/3 of a pound. So we have: [B]y = 2/3x + 7 [/B] The baby starts off with 7 pounds. So we add 7 pounds + 2/3 times the number of months passed since birth.
A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going dow
A motorboat travels 408 kilometers in 8 hours going upstream and 546 kilometers in 6 hours going downstream. What is the rate of the boat in still water and what is the rate of the current? [U]Assumptions:[/U] [LIST] [*]B = the speed of the boat in still water. [*]S = the speed of the stream [/LIST] Relative to the bank, the speeds are: [LIST] [*]Upstream is B - S. [*]Downstream is B + S. [/LIST] [U]Use the Distance equation: Rate * Time = Distance[/U] [LIST] [*]Upstream: (B-S)6 = 258 [*]Downstream: (B+S)6 = 330 [/LIST] Simplify first by dividing each equation by 6: [LIST] [*]B - S = 43 [*]B + S = 55 [/LIST] Solve this system of equations by elimination. Add the two equations together: (B + B) + (S - S) = 43 + 55 Cancelling the S's, we get: 2B = 98 Divide each side by 2: [B]B = 49 mi/hr[/B] Substitute this into either equation and solve for S. B + S = 55 49 + S = 55 To solve this, we [URL='https://www.mathcelebrity.com/1unk.php?num=49%2Bs%3D55&pl=Solve']type it in our search engine[/URL] and we get: S = [B]6 mi/hr[/B]
A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pa
A motorist pays $4.75 per day in tolls to travel to work. He also has the option to buy a monthly pass for $80. How many days must he work (i.e. pass through the toll) in order to break even? Let the number of days be d. Break even means both costs are equal. We want to find when: 4.75d = 80 To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.75d%3D80&pl=Solve']type this equation into our search engine[/URL] and we get: d = 16.84 days We round up to an even [B]17 days[/B].
A movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an
A movie theater charges $7 for adults and $3 for seniors on a particular day when 324 people paid an admission the total receipts were 1228 how many were seniors and how many were adults? Let the number of adult tickets be a. Let the number of senior tickets be s. We're given two equations: [LIST=1] [*]a + s = 324 [*]7a + 3s = 1228 [/LIST] We have a set of simultaneous equations we can solve using 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+324&term2=7a+%2B+3s+%3D+1228&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [LIST] [*][B]a = 64[/B] [*][B]s = 260[/B] [/LIST]
A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid
A movie theater charges 7.00 for adults and 2.00 for seniors citizens. On a day when 304 people paid for admission, the total receipt were 1118. How many who paid were adults ? How many were senior citizens? Let a be the number of adult tickets. Let s be the number of senior citizen tickets. We're given two equations: [LIST=1] [*]a + s = 304 [*]7a + 2s = 1118 [/LIST] We can solve this system of equations three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+304&term2=7a+%2B+2s+%3D+1118&pl=Cramers+Method']Cramer's Method[/URL] [/LIST] No matter which way we choose, we end up with the same answer: [LIST] [*]a = [B]102[/B] [*]s = [B]202[/B] [/LIST]
A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for stu
A movie theater has a seating capacity of 143. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1030, How many children, students, and adults attended? Let c be the number of children's tickets, s be the number of student's tickets, and a be the number of adult's tickets. We have 3 equations: [LIST=1] [*]a + c + s = 143 [*]a = 0.5c [*]12a + 5c + 7s =1030 [/LIST] Substitute (2) into (1) 0.5c + c + s = 143 1.5c + s = 143 Subtract 1.5c from each side 4. s = 143 - 1.5c Now, take (4) and (2), and plug it into (3) 12(0.5c) + 5c + 7(143 - 1.5c) = 1030 6c + 5c + 1001 - 10.5c = 1030 Combine like terms: 0.5c + 1001 = 1030 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.5c%2B1001%3D1030&pl=Solve']equation calculator[/URL] to get [B]c = 58[/B]. Plug this back into (2) a = 0.5(58) [B]a = 29 [/B] Now take the a and c values, and plug it into (1) 29 + 58 + s = 143 s + 87 = 143 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=s%2B87%3D143&pl=Solve']equation calculator[/URL] again, we get [B]s = 56[/B]. To summarize, we have: [LIST] [*]29 adults [*]58 children [*]56 students [/LIST]
A music app charges $2 to download the app plus $1.29 per song download. Write and solve a linear eq
A music app charges $2 to download the app plus $1.29 per song download. Write and solve a linear equation to find the total cost to download 30 songs Set up the cost function C(s) where s is the number of songs: C(s) = cost per song * s + download fee Plugging in our numbers for s = 30 and a download fee of $2 and s = 1.29, we have: C(30) = 1.29(30) + 2 C(30) = 38.7 + 2 C(30) = [B]40.7[/B]
A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear
A music app charges $2 to download the app plus $1.29 per song downloaded. Write and solve a linear equation to find the total cost to download 30 songs. Let the number of songs be s. And the cost function be C(s). We have: C(s) = Price per song downloaded * s + app download charge C(s) = 1.29s + 2 The problem asks for C(30): C(3) = 1.29(30) + 2 C(3) = 38.7 +2 C(3) = $[B]40.7[/B]
a music app charges $5 to download the app plus $1.25 per song downloaded. write linear equation to
a music app charges $5 to download the app plus $1.25 per song downloaded. write linear equation to calculate the cost for x number of songs With x songs, our Cost equation C(x) is: C(x) = cost per download * x downloads + app download fee [B]C(x) = 1.25x + 5[/B]
A music app charges 2$ to download the app plus 1.29$ per song download. Write and solve linear equa
A music app charges 2$ to download the app plus 1.29$ per song download. Write and solve linear equation and a linear equation to find the total cost to download 30 songs Set up the equation C(d) where d is the number of downloads: C(d) = cost per download * d + download fee Plugging in our numbers, we get: C(d) = 1.29d + 2 The problem asks for C(30): C(30) = 1.29(30) + 2 C(30) = 38.7 + 2 C(30) = [B]40.70[/B]
A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the c
A new car worth $30,000 is depreciating in value by $3,000 per year. After how many years will the cars value be $9,000 Step 1, the question asks for Book Value. Let y be the number of years since purchase. We setup an equation B(y) which is the Book Value at time y. B(y) = Sale Price - Depreciation Amount * y We're given Sale price = $30,000, depreciation amount = 3,000, and B(y) = 9000 30000 - 3000y = 9000 To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=30000-3000y%3D9000&pl=Solve']type this in our math engine[/URL] and we get: y = [B]7 [/B] To check our work, substitute y = 7 into B(y) B(7) = 30000 - 3000(7) B(7) = 30000 - 21000 B(7) = 9000 [MEDIA=youtube]oCpBBS7fRYs[/MEDIA]
a number is twice another number
a number is twice another number The phrase [I]a number[/I] means an arbitrary variable, let's call it x The phrase [I]another number [/I]means another arbitrary variable, let's call it y Twice means we multiply y by 2: 2y The phrase [I]is [/I]means an equation, so we set x equal to 2y: [B]x = 2y[/B]
A number multiplied by 6 and divided by 5 give four more than a number?
A number multiplied by 6 and divided by 5 give four more than a number? A number is represented by an arbitrary variable, let's call it x. Multiply by 6: 6x Divide by 5 6x/5 The word "gives" means equals, so we set this equal to 4 more than a number, which is x + 4. 6x/5 = x + 4 Now, multiply each side of the equation by 5, to eliminate the fraction on the left hand side: 6x(5)/5 = 5(x + 4) The 5's cancel on the left side, giving us: 6x = 5x + 20 Subtract 5x from each side [B]x = 20[/B] Check our work from our original equation: 6x/5 = x + 4 6(20)/5 ? 20 + 4 120/5 ?24 24 = 24 <-- Yes, we verified our answer
A number n diminished by 8 gives 12
A number n diminished by 8 gives 12 A number n can be written as n: n Diminished by means we subtract, so we subtract 8 from n: n - 8 The word [I]gives[/I] means an equation, so we set n - 8 equal to 12: [B]n - 8 = 12[/B]
A parabola has a Vertex at (4,-2) and a Focus at (6,-2). Find the equation of the parabola
A parabola has a Vertex at (4,-2) and a Focus at (6,-2). Find the equation of the parabola and the lotus rectum. Equation of a parabola given the vertex and focus is: ([I]x[/I] � [I]h[/I])^2 = 4[I]p[/I]([I]y[/I] � [I]k[/I]) The vertex (h, k) is 4, -2 The distance is p, and since the y coordinates of -2 are equal, the distance is 6 - 4 = 2. So p = 2 Our parabola equation becomes: (x - 4)^2 = 4(2)(y - -2) [B](x - 4)^2 = 8(y + 2)[/B] Latus rectum of a parabola is 4p, where p is the distance between the vertex and the focus LR = 4p LR = 4(2) [B]LR = 8[/B]
A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. Wh
A parallelogram has a perimeter of 54 centimeters. Two of the sides are each 17 centimeters long. What is the length of each of the other two sides? A parallelogram is a rectangle bent on it's side. So we have the perimeter formula P below: P = 2l + 2w We're given w = 17 and P = 54. So we plug this into the formula for perimeter: 2l + 2(17) = 54 2l + 34 = 54 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B34%3D54&pl=Solve']equation calculator[/URL], we get [B]l = 10[/B].
A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of
A parking meter contains 27.05 in quarters and dimes. All together there are 146 coins. How many of each coin are there? Let d = the number of dimes and q = the number of quarters. We have two equations: (1) d + q = 146 (2) 0.1d + 0.25q = 27.05 Rearrange (1) into (3) solving for d (3) d = 146 - q Substitute (3) into (2) 0.1(146 - q) + 0.25q = 27.05 14.6 - 0.1q + 0.25q = 27.05 Combine q's 0.15q + 14.6 = 27.05 Subtract 14.6 from each side 0.15q = 12.45 Divide each side by 0.15 [B]q = 83[/B] Plugging that into (3), we have: d = 146 - 83 [B]d = 63[/B]
A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables
A party rental company has chairs and tables for rent. The total cost to rent 5 chairs and 3 tables is $37. The total cost to rent 2 chairs and 6 tables is $64. What is the cost to rent each chair and each table? Let c be the cost of renting one chair and t be the cost of renting one table. We're given two equations: [LIST=1] [*]5c + 3t = 37 [*]2c + 6t =64 [/LIST] We have a system of equations. Using our system of equations calculator, we can solve this problem any of 3 ways below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5c+%2B+3t+%3D+37&term2=2c+%2B+6t+%3D+64&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] All 3 methods give the same answer: [LIST] [*][B]Chairs (c) cost $1.25[/B] [*][B]Tables (t) cost $10.25[/B] [/LIST]
A pawn broker buys a tv and a computer for $600. He sells the computer at a markup of 30% and the tv
A pawn broker buys a tv and a computer for $600. He sells the computer at a markup of 30% and the tv at a markup of 20%. If he makes a profit of $165 on the sale of the two items, what did he pay for the computer? Let c be the price of the computer and t be the price of the tv. WE have: [LIST=1] [*]c + t = 600 [*]c(1.3) + t(1.2) = 765 <-- (600 + 165 profit) [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+600&term2=1.3c+%2B+1.2t+%3D+765&pl=Cramers+Method']simultaneous equation calculator[/URL], we get: [B]c = 450[/B] t = 150
A person has $13,000 invested in stock A and stock B. Stock A currently sells for $20 a share and
A person has $13,000 invested in stock A and stock B. Stock A currently sells for $20 a share and stock B sells for $90 a share. If stock B triples in value and stock A goes up 50%, his stock will be worth $33,000. How many shares of each stock does he own? Set up the given equations, where A is the number of shares for Stock A, and B is the number of shares for Stock B [LIST=1] [*]90A + 20B = 13000 [*]3(90A) + 1.5(20B) = 33000 <-- [I]Triple means multiply by 3, and 50% gain means multiply by 1.5[/I] [/LIST] Rewrite (2) by multiplying through: 270A + 30B = 33000 Using our simultaneous equations calculator, we get [B]A = 100 and B = 200[/B]. Click the links below to solve using each method: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=90A+%2B+20B+%3D+13000&term2=270A+%2B+30B+%3D+33000&pl=Cramers+Method']Cramers Method[/URL] [/LIST] Check our work using equation (1) 90(100) + 20(200) ? 13,000 9000 + 4000 ? 13,000 13000 = 13000
A person invested 30,000 in stocks and bonds. Her investment in bonds is 2000 more than 1-third her
A person invested 30,000 in stocks and bonds. Her investment in bonds is 2000 more than 1-third her investments in stocks. How much did she invest in stocks? How much did she invest in bonds? Let the stock investment be s, and the bond investment be b. We're given: [LIST=1] [*]b + s = 30000 [*]b = 1/3s + 2000 [/LIST] Plug in (2) to (1): 1/3s + 2000 + s = 30000 Group like terms: (1/3 + 1)s + 2000 = 30000 Since 1 = 3/3, we have: 4/3s + 2000 = 30000 Subtract 2000 from each side: 4/3s + 2000 - 2000 = 30000 - 2000 Cancel the 2000's on the left side, we get: 4/3s = 28000 [URL='https://www.mathcelebrity.com/1unk.php?num=4%2F3s%3D28000&pl=Solve']Typing this equation into our calculator[/URL], we get: s = [B]21,000[/B]
A person will devote 31 years to be sleeping and watching tv. The number of years sleeping will exce
A person will devote 31 years to be sleeping and watching tv. The number of years sleeping will exceed the number of years watching tv by 19. How many years will the person spend on each of these activities Let s be sleeping years and t be tv years, we have two equations: [LIST=1] [*]s + t = 31 [*]s = t + 19 [/LIST] Substitute (2) into (1) (t + 19) + t = 31 Combine like terms: 2t + 19 = 31 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2t%2B19%3D31&pl=Solve']equation solver[/URL], we get [B]t = 6[/B]. Using equation (2), we have s = 6 + 19 s = [B]25[/B]
A person works 46 hours in one week and earns 440 dollars. They get time and a half for over 40 hour
A person works 46 hours in one week and earns 440 dollars. They get time and a half for over 40 hours. What is their hourly salary? Let the hourly rate be r. Since time and a half is 1.5 the hourly rate, We're given: 40r + 6(1.5r) = 440 40r + 9r = 440 to solve this equation for r, we type it in our search engine and we get: r = [B]$8.98[/B]
A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the custome
A phone company offers two monthly charge plans. In Plan A, there is no monthly fee, but the customer pays 8 cents per minute of use. In Plan B, the customer pays a monthly fee of $1.50 and then an additional 7 cents per minute of use. For what amounts of monthly phone use will Plan A cost more than Plan B? Set up the cost equations for each plan. The cost equation for the phone plans is as follows: Cost = Cost Per Minute * Minutes + Monthly Fee Calculate the cost of Plan A: Cost for A = 0.08m + 0. <-- Since there's no monthly fee Calculate the cost of Plan B: Cost for B = 0.07m + 1.50 The problem asks for what amounts of monthly phone use will Plan A be more than Plan B. So we set up an inequality: 0.08m > 0.07m + 1.50 [URL='https://www.mathcelebrity.com/1unk.php?num=0.08m%3E0.07m%2B1.50&pl=Solve']Typing this inequality into our search engine[/URL], we get: [B]m > 150 This means Plan A costs more when you use more than 150 minutes per month.[/B]
A piggy bank contains $90.25 in dimes and quarters. Which equation represents this scenario? Let x r
A piggy bank contains $90.25 in dimes and quarters. Which equation represents this scenario? Let x represent the number of dimes, and let y represent the number of quarters. Since amount = cost * quantity, we have: [B]0.1d + 0.25q = 90.25[/B]
A pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarte
A pile of coins, consisting of quarters and half dollars, is worth 11.75. If there are 2 more quarters than half dollars, how many of each are there? Let h be the number of half-dollars and q be the number of quarters. Set up two equations: (1) q = h + 2 (2) 0.25q + 0.5h = 11.75 [U]Substitute (1) into (2)[/U] 0.25(h + 2) + 0.5h = 11.75 0.25h + 0.5 + 0.5h = 11.75 [U]Group h terms[/U] 0.75h + 0.5 = 11.75 [U]Subtract 0.5 from each side[/U] 0.75h = 11.25 [U]Divide each side by h[/U] [B]h = 15[/B] [U]Substitute h = 15 into (1)[/U] q = 15 + 2 [B]q = 17[/B]
A plant is 15 cm high and grows 4.5 cm every month. How many months will it take until the plant is
A plant is 15 cm high and grows 4.5 cm every month. How many months will it take until the plant is 27.5 cm We set up the height function H(m) where m is the number of months since now. We have: H(m) = 4.5m + 15 We want to know when H(m) = 27.5, so we set our H(m) function equal to 27.5: 4.5m + 15 = 27.5 To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=4.5m%2B15%3D27.5&pl=Solve']type this equation into our search engine[/URL] and we get: m = 2.78 So we round up to [B]3 whole months[/B]
A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, r
A police officer is trying to catch a fleeing criminal. The criminal is 20 feet away from the cop, running at a rate of 5 feet per second. The cop is running at a rate of 6.5 feet per second. How many seconds will it take for the police officer to catch the criminal? Distance = Rate * Time [U]Criminal:[/U] 5t + 20 [U]Cop[/U]: 6.5t We want to know when their distances are the same (cop catches criminal). So we set the equations equal to each other: 5t + 20 = 6.5t To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=5t%2B20%3D6.5t&pl=Solve']we type it in our search engine[/URL] and we get: t = 13.333 seconds
A population grows at 6% per year. How many years does it take to triple in size?
A population grows at 6% per year. How many years does it take to triple in size? With a starting population of P, and triple in size means 3 times the original, we want to know t for: P(1.06)^t = 3P Divide each side by P, and we have: 1.06^t = 3 Typing this equation into our search engine to solve for t, we get: t = [B]18.85 years[/B] Note: if you need an integer answer, we round up to 19 years
A pound of chocolate costs 6 dollars. Greg buys p pounds. Write an equation to represent the total c
A pound of chocolate costs 6 dollars. Greg buys p pounds. Write an equation to represent the total cost c that Greg pays Since cost = price * quantity, we have: [B]c = 6p[/B]
A pound of chocolate costs 6 dollars. Ryan buys p pounds. Write an equation to represent the total c
A pound of chocolate costs 6 dollars. Ryan buys p pounds. Write an equation to represent the total cost c that Ryan pays Since cost = Price * Quantity, we have: [B]c = 6p[/B]
A pound of chocolate costs 7 dollars. Hong buys p pounds . Write an equation to represent the total
A pound of chocolate costs 7 dollars. Hong buys p pounds . Write an equation to represent the total cost c that Hong pays Our equation is the cost of chocolate multiplied by the number of pounds: [B]c = 7p[/B]
A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages?
A printer can print 25 pages per minute. At this rate, how long will it take to print 2000 pages? Let m be the number of minutes it takes to print 2,000 pages. We have the equation: 25m = 2000 [URL='https://www.mathcelebrity.com/1unk.php?num=25m%3D2000&pl=Solve']Type this equation into our search engine[/URL], and we get: m = 80
A printer prints 2 photos each minute. Let P be the number of photos printed in M minutes. Write an
A printer prints 2 photos each minute. Let P be the number of photos printed in M minutes. Write an equation relating P to M. Set up the equation P(M). [B]P(M) = 2M[/B] Read this as for every minute that goes by, 2 photos are printed.
A private high school charges $52,200 for tuition, but this figure is expected to rise 7% per year.
A private high school charges $52,200 for tuition, but this figure is expected to rise 7% per year. What will tuition be in 3 years? We have the following appreciation equation A(y) where y is the number of years: A(y) = Initial Balance * (1 + appreciation percentage)^ years Appreciation percentage of 7% is written as 0.07, so we have: A(3) = 52,200 * (1 + 0.07)^3 A(3) = 52,200 * (1.07)^3 A(3) = 52,200 * 1.225043 A(3) = [B]63,947.25[/B]
A private jet flies the same distance in 4 hours that a commercial jet flies in 2 hours. If the spee
A private jet flies the same distance in 4 hours that a commercial jet flies in 2 hours. If the speed of the commercial jet was 154 mph less than 3 times the speed of the private jet, find the speed of each jet. Let p = private jet speed and c = commercial jet speed. We have two equations: (1) c = 3p - 154 (2) 4p =2c Plug (1) into (2): 4p = 2(3p - 154) 4p = 6p - 308 Subtract 4p from each side: 2p - 308 = 0 Add 308 to each side: 2p = 308 Divide each side by 2: [B]p = 154[/B] Substitute this into (1) c = 3(154) - 154 c = 462 - 154 [B]c = 308[/B]
A problem states: "There are 9 more children than parents in a room. There are 25 people in the room
A problem states: "There are 9 more children than parents in a room. There are 25 people in the room in all. How many children are there in the room?" Let the number of children be c. Let the number of parents be p We're given: [LIST=1] [*]c = p + 9 [I](9 more children than parents)[/I] [*]c + p = 25 [/LIST] to solve this system of equations, we plug equation (1) into equation (2) for c: (p + 9) + p = 25 Group like terms: 2p + 9 = 25 To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=2p%2B9%3D25&pl=Solve']type it in our search engine[/URL] and we get: p = [B]8[/B]
A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for
A promotional deal for long distance phone service charges a $15 basic fee plus $0.05 per minute for all calls. If Joe's phone bill was $60 under this promotional deal, how many minutes of phone calls did he make? Round to the nearest integer if necessary. Let m be the number of minutes Joe used. We have a cost function of: C(m) = 0.05m + 15 If C(m) = 60, then we have: 0.05m + 15 = 60 [URL='https://www.mathcelebrity.com/1unk.php?num=0.05m%2B15%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get: m = [B]900[/B]
A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you ge
A rational number is such that when you multiply it by 7/3 and subtract 3/2 from the product, you get 92. What is the number? Let the rational number be x. We're given: 7x/3 - 3/2 = 92 Using a common denominator of 3*2 = 6, we rewrite this as: 14x/6 - 9/6 = 92 (14x - 9)/6 = 92 Cross multiply: 14x - 9 = 92 * 6 14x - 9 = 552 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=14x-9%3D552&pl=Solve']type this equation into our search engine [/URL]and we get: x = [B]40.07[/B]
a recipe of 20 bread rolls requires 5 tablespoons of butter. How many tablespoons of butter are need
a recipe of 20 bread rolls requires 5 tablespoons of butter. How many tablespoons of butter are needed for 30 bread rolls? Set up a proportion of bread rolls per tablespoons of butter where t is the amount of tablespoons of butter needed for 30 bread rolls: 20/5 = 30/t Cross multiply our proportion: Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2 20t = 30 * 5 20t = 150 Divide each side of the equation by 20: 20t/20 = 150/20 Cancel the 20's on the left side and we get: t = [B]7.5[/B]
A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSION
A RECTANGLE HAS A PERIMETER OF 196 CENTIMETERS. IF THE LENGTH IS 6 TIMES ITS WIDTH FIND TH DIMENSIONS OF THE RECTANGLE? Whoa... stop screaming with those capital letters! But I digress... The perimeter of a rectangle is: P = 2l + 2w We're given two equations: [LIST=1] [*]P = 196 [*]l = 6w [/LIST] Plug these into the perimeter formula: 2(6w) + 2w = 196 12w + 2w = 196 [URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B2w%3D196&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]w = 14[/B] Now we put w = 14 into equation (2) above: l = 6(14) [B]l = 84 [/B] So our length (l), width (w) of the rectangle is (l, w) = [B](84, 14) [/B] Let's check our work by plugging this into the perimeter formula: 2(84) + 2(14) ? 196 168 + 28 ? 196 196 = 196 <-- checks out
a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions?
a rectangle has an area of 238 cm 2 and a perimeter of 62 cm. What are its dimensions? We know the rectangle has the following formulas: Area = lw Perimeter = 2l + 2w Given an area of 238 and a perimeter of 62, we have: [LIST=1] [*]lw = 238 [*]2(l + w) = 62 [/LIST] Divide each side of (1) by w: l = 238/w Substitute this into (2): 2(238/w + w) = 62 Divide each side by 2: 238/w + w = 31 Multiply each side by w: 238w/w + w^2 = 31w Simplify: 238 + w^2 = 31w Subtract 31w from each side: w^2 - 31w + 238 = 0 We have a quadratic. So we run this through our [URL='https://www.mathcelebrity.com/quadratic.php?num=w%5E2-31w%2B238%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL] and we get: w = (14, 17) We take the lower amount as our width and the higher amount as our length: [B]w = 14 l = 17 [/B] Check our work for Area: 14(17) = 238 <-- Check Check our work for Perimeter: 2(17 + 14) ? 62 2(31) ? 62 62 = 62 <-- Check
A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards b
A rectangle shaped parking lot is to have a perimeter of 506 yards. If the width must be 100 yards because of a building code, what will the length need to be? Perimeter of a rectangle (P) with length (l) and width (w) is: 2l + 2w = P We're given P = 506 and w = 100. We plug this in to the perimeter formula and get: 2l + 2(100) = 506 To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B2%28100%29%3D506&pl=Solve']type it in our search engine[/URL] and we get: l = [B]153[/B]
A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 fe
A rectangular field is to be enclosed with 1120 feet of fencing. If the length of the field is 40 feet longer than the width, then how wide is the field? We're given: [LIST=1] [*]l = w + 40 [/LIST] And we know the perimeter of a rectangle is: P = 2l + 2w Substitute (1) into this formula as well as the given perimeter of 1120: 2(w + 40) + 2w = 1120 Multiply through and simplify: 2w + 80 + 2w = 1120 Group like terms: 4w + 80 = 1120 [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B80%3D1120&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 260[/B]
A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find i
A rectangular football pitch has its length equal to twice its width and a perimeter of 360m. Find its length and width. The area of a rectangle (A) is: A = lw --> where l is the length and w is the width We're given l = 2w, so we substitute this into the Area equation: A = (2w)w A = 2w^2 We're given the area of the pitch is 360, so we set: 2w^2 = 360 We [URL='https://www.mathcelebrity.com/1unk.php?num=2w%5E2%3D360&pl=Solve']type this equation into our search engine[/URL], follow the links, and get: w = [B]6*sqrt(5) [/B] Now we take this, and substitute it into this equation: 6*sqrt(5)l = 360 Dividing each side by 6*sqrt(5), we get: l = [B]60/sqrt(5)[/B]
A rectangular garden is 5 ft longer than it is wide. Its area is 546 ft2. What are its dimensions?
A rectangular garden is 5 ft longer than it is wide. Its area is 546 ft2. What are its dimensions? [LIST=1] [*]Area of a rectangle is lw. lw = 546ft^2 [*]We know that l = w + 5. [/LIST] Substitute (2) into (1) (w + 5)w = 546 w^2 + 5w = 546 Subtract 546 from each side w^2 + 5w - 546 = 0 Using the positive root in our [URL='http://www.mathcelebrity.com/quadratic.php?num=w%5E2%2B5w-546%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get [B]w = 21[/B]. This means l = 21 + 5. [B]l = 26[/B]
A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards
A rectangular parking lot has a perimeter of 152 yards. If the length of the parking lot is 12 yards greater than the width. What is the width of the parking lot? The perimeter of a rectangle is: 2l + 2w = P. We're given 2 equations: [LIST=1] [*]2l + 2w = 152 [*]l = w + 12 [/LIST] Substitute equation (2) into equation (1) for l: 2(w + 12) + 2w = 152 2w + 24 + 2w = 152 Combine like terms: 4w + 24 = 152 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B24%3D152&pl=Solve']type this equation into our search engine[/URL] and we get: w =[B] 32[/B]
A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters
A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters Given l = length and w = width, The perimeter of a rectangle is 2l + 2w, we have: [LIST=1] [*]l = 3w [*]2l + 2w = 56 [/LIST] Substitute equation (1) into equation (2) for l: 2(3w) + 2w = 56 6w + 2w = 56 To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our math engine[/URL] and we get: w = [B]7 [/B] To solve for l, we substitute w = 7 into equation (1): l = 3(7) l = [B]21[/B]
A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters.
A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. We're given the following: [LIST] [*]l = 3w [/LIST] We know the Perimeter (P) of a rectangle is: P = 2l + 2w Substituting l = 3w and P = 56 into this equation, we get: 2(3w) + 2w = 56 Multiplying through, we get: 6w + 2w = 56 (6 +2)w = 56 8w = 56 [URL='https://www.mathcelebrity.com/1unk.php?num=8w%3D56&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 7[/B] Substitute w = 7 into l = 3w, we get: l = 3(7) [B]l = 21[/B]
A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimens
A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimensions of the room. We're given two items: [LIST] [*]l = 3w [*]P = 56 [/LIST] We know the perimeter of a rectangle is: 2l + 2w = P We plug in the given values l = 3w and P = 56 to get: 2(3w) + 2w = 56 6w + 2w = 56 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']plug this equation into our search engine[/URL] and we get: w = [B]7 [/B] To solve for l, we plug in w = 7 that we just found into the given equation l = 3w: l = 3(7) l = [B]21 [/B] So our dimensions length (l) and width (w) are: (l, w) = [B](21, 7)[/B]
A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimens
A rectangular room is 3 times as long as it is wide, and its perimeter is 56 meters. Find the dimension of the room. We're given: l = 3w The Perimeter (P) of a rectangle is: P = 2l + 2w With P = 56, we have: [LIST=1] [*]l = 3w [*]2l + 2w = 56 [/LIST] Substitute equation (1) into equation (2) for l: 2(3w) + 2w = 56 6w + 2w = 56 To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D56&pl=Solve']type it in our search engine[/URL] and we get: w = [B]7 [/B] Now we plug w = 7 into equation (1) above to solve for l: l = 3(7) l = [B]21[/B]
A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimens
A rectangular room is 3 times as long as it is wide, and its perimeter is 64 meters. Find the dimension of the room. We're given: [LIST] [*]l = 3w [*]P = 64 [/LIST] We also know the perimeter of a rectangle is: 2l + 2w = P We plugin l = 3w and P = 64 into the perimeter equation: 2(3w) + 2w = 64 Multiply through to remove the parentheses: 6w + 2w = 64 To solve this equation for w, we type it in our search engine and we get: [B]w = 8[/B] To solve for l, we plug w = 8 into the l = 3w equation above: l = 3(8) [B]l = 24[/B]
A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimens
A rectangular room is 4 times as long as it is wide, and its perimeter is 80 meters. Find the dimension of the room The perimeter of a rectangle is P = 2l + 2w. We're given two equations: [LIST=1] [*]l = 4w [*]2l + 2w = 80. <-- Since perimeter is 80 [/LIST] Plug equation (1) into equation (2) for l: 2(4w) + 2w = 80 8w + 2w = 80 [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B2w%3D80&pl=Solve']Plugging this equation into our search engine[/URL], we get: w = [B]10[/B] To get l, we plug w = 10 into equation (1): l = 4(10) l = [B]40[/B]
A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation t
A rental truck costs $49.95+$0.59 per mile and another costs $39.95 plus $0.99, set up an equation to determine the break even point? Set up the cost functions for Rental Truck 1 (R1) and Rental Truck 2 (R2) where m is the number of miles R1(m) = 0.59m + 49.95 R2(m) = 0.99m + 39.95 Break even is when we set the cost functions equal to one another: 0.59m + 49.95 = 0.99m + 39.95 [URL='https://www.mathcelebrity.com/1unk.php?num=0.59m%2B49.95%3D0.99m%2B39.95&pl=Solve']Typing this equation into the search engine[/URL], we get [B]m = 25[/B].
A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write an
A repair bill for a car is $648.45. The parts cost $265.95. The labor cost is $85 per hour. Write and solve an equation to find the number of hours spent repairing the car. Let h be the number of hours spent repairing the car. We set up the cost function C(h): C(h) = Labor Cost per hour * h + Parts Cost We're given C(h) = 648.85, parts cost = 265.95, and labor cost per hour of 85, so we have: 85h + 265.95 = 648.85 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=85h%2B265.95%3D648.85&pl=Solve']type this into our search engine[/URL] and we get: h = [B]4.5[/B]
A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and s
A repair bill for your car is $553. The parts cost $265. The labor cost is $48 per hour. Write and solve an equation to find the number of hours of labor spent repairing the car Set up the cost equation C(h) where h is the number of labor hours: C(h) = Labor Cost per hour * h + Parts Cost We're given C(h) = 553, Parts Cost = 265, and Labor Cost per Hour = 48. So we plug these in: 48h + 265 = 553 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=48h%2B265%3D553&pl=Solve']type it in our math engine[/URL] and we get: h = [B]6 hours[/B]
A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the am
A restaurant earns $1073 on Friday and $1108 on Saturday. Write and solve an equation to find the amount x (in dollars) the restaurant needs to earn on Sunday to average $1000 per day over the three-day period. Let Sunday's earnings be s. With 3 days, we divide our sum of earnings for 3 days by 3 to get our 1,000 average, so we have: (1073 + 1108 + s)/3 = 1000 Cross multiply: 1073 + 1108 + s = 1000 * 3 1073 + 1108 + s = 3000 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=1073%2B1108%2Bs%3D3000&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]819[/B]
A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment
A retired couple invested $8000 in bonds. At the end of one year, they received an interest payment of $584. What was the simple interest rate of the bonds? For simple interest, we have: Balance * interest rate = Interest payment 8000i = 584 Divide each side of the equation by 8000 to isolate i: 8000i/8000 = 584/8000 Cancelling the 8000's on the left side, we get: i = 0.073 Most times, interest rates are expressed as a percentage. Percentage interest = Decimal interest * 100% Percentage interest = 0.073 * 100% Multiplying by 100 is the same as moving the decimal point two places right: Percentage interest = [B]7.3%[/B]
A revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break-even point is
A revenue function is R(x) = 22x and a cost function is C(x) = -9x + 341. The break-even point is Break even is when C(x) = R(x). So we set them equal and solve for x: -9x + 341 = 22x Typing[URL='https://www.mathcelebrity.com/1unk.php?num=-9x%2B341%3D22x&pl=Solve'] this equation into our search engine[/URL], we get: x = [B]11[/B]
a rocket is propelled into the air. its path can be modelled by the relation h = -5t^2 + 50t + 55, w
a rocket is propelled into the air. its path can be modeled by the relation h = -5t^2 + 50t + 55, where t is the time in seconds, and h is height in metres. when does the rocket hit the ground We set h = 0: -5t^2 + 50t + 55 = 0 Typing this quadratic equation into our search engine to solve for t, we get: t = {-1, 11} Time can't be negative, so we have: t = [B]11[/B]
a sales rep can generate $1,900,000 in business annually. What rate of commission does he need to ea
a sales rep can generate $1,900,000 in business annually. What rate of commission does he need to earn $30,000? We need a commission percent p where: 1900000 * p = 30000 To solve for p, we type this equation into our search engine and we get: p = 0.0158 or [B]1.58%[/B]
A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is
A salesperson works 40 hours per week at a job where he has two options for being paid. Option A is an hourly wage of $24. Option B is a commission rate of 4% on weekly sales. How much does he need to sell this week to earn the same amount with the two options? Option A payment function: 24h With a 40 hour week, we have: 24 * 40 = 960 Option B payment function with sales amount (s): 0.04s We want to know the amount of sales (s) where Option A at 40 hours = Option B. So we set both equal to each other: 0.04s = 960 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.04s%3D960&pl=Solve']type it in our math engine[/URL] and we get: s = [B]24,000[/B]
A school dance had 675 cookies each student took 3 cookies and there were 15 cookies leftover how ma
A school dance had 675 cookies each student took 3 cookies and there were 15 cookies leftover how many students attended the dance Let each student be s. We have: 3s + 15 = 675 To solve this equation for s, [URL='https://www.mathcelebrity.com/1unk.php?num=3s%2B15%3D675&pl=Solve']we type it in our search engine[/URL] and we get: s = [B]220[/B]
A school theater group is selling candy to raise funds in order to put on their next performance. Th
A school theater group is selling candy to raise funds in order to put on their next performance. The candy cost the group $0.20 per piece. Plus, there was a $9 shipping and handling fee. The group is going to sell the candy for $0.50 per piece. How many pieces of candy must the group sell in order to break even? [U]Set up the cost function C(p) where p is the number of pieces of candy.[/U] C(p) = Cost per piece * p + shipping and handling fee C(p) = 0.2p + 9 [U]Set up the Revenue function R(p) where p is the number of pieces of candy.[/U] R(p) = Sale price * p R(p) = 0.5p Break-even means zero profit or loss, so we set the Cost Function equal to the Revenue Function 0.2p + 9 = 0.5p To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B9%3D0.5p&pl=Solve']type it in our math engine[/URL] and we get: p = [B]30[/B]
A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number?
A secret number is added to 6. The total is multiplied by 5 to get 50. What is the secret number? Take this algebraic expression in pieces: [LIST] [*]Let the secret number be n. [*]Added to means we add 6 to n: n + 6 [*]The total is multiplied by 5: 5(n + 6) [*]The phrase [I]to get[/I] means equal to, so we set 5(n + 6) equal to 50 [/LIST] 5(n + 6) = 50 To solve this equation for n, we type it in our search engine and we get: n = [B]4[/B]
A service charges a $1.95 flat rate plus $0.05 per mile . Jason only has $12 to spend on a a ride
A service charges a $1.95 flat rate plus $0.05 per mile. Jason only has $12 to spend on a a ride. Set up the cost equation C(m) where m is the number of miles: C(m) = 0.05m + 1.95 The problems asks for the number of miles (m) when C(m) = 12: 0.05m + 1.95 = 12 [URL='https://www.mathcelebrity.com/1unk.php?num=0.05m%2B1.95%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get: m = [B]201[/B]
A set of 4 consecutive integers adds up to 314. What is the least of the 4 integers?
A set of 4 consecutive integers adds up to 314. What is the least of the 4 integers? First integer is x. The next 3 are x + 1, x + 2, and x + 3. Set up our equation: x + (x + 1) + (x + 2) + (x + 3) = 314 Group x terms and group constnats (x + x + x + x) + (1 + 2 + 3) = 314 Simplify and combine 4x + 6 = 314 [URL='http://www.mathcelebrity.com/1unk.php?num=4x%2B6%3D314&pl=Solve']Enter this in the equation solver[/URL] [B]x = 77[/B]
A set of data has a range of 30. The least value in the set of data is 22. What is the greatest valu
A set of data has a range of 30. The least value in the set of data is 22. What is the greatest value in the set of data? High Value - Low Value = Range Let the high value be h. We're given: h - 22 = 30 We [URL='https://www.mathcelebrity.com/1unk.php?num=h-22%3D30&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]52[/B]
A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package
A shipping service charges $0.43 for the first ounce and $0.29 for each additional ounce of package weight. Write an equation to represent the price P of shipping a package that weighs x ounces, for any whole number of ounces greater than or equal to 1. Set up the price function P(x) [B]P(x) = 0.43 + 0.29(x - 1)[/B]
A social networking site currently has 38,000 active members per month, but that figure is dropping
A social networking site currently has 38,000 active members per month, but that figure is dropping by 5% with every month that passes. How many active members can the site expect to have in 7 months? Setup an equation S(m) where m is the number of months that pass: S(m) = 38000 * (1 - 0.05)^t S(m) = 38000 * (0.95)^t The problem asks for S(7): S(7) = 38000 * (0.95)^7 S(7) = 38000 * (0.69833729609) S(7) = 26,536.82 We round down to a full person and get: S(7) = [B]26,536[/B]
a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age.
a son is 1/4 of his fathers age. the difference in their ages is 30. what is the fathers age. Declare variables: [LIST] [*]Let f be the father's age [*]Let s be the son's age [/LIST] We're given two equations: [LIST=1] [*]s = f/4 [*]f - s = 30. [I]The reason why we subtract s from f is the father is older[/I] [/LIST] Using substitution, we substitute equaiton (1) into equation (2) for s: f - f/4 = 30 To remove the denominator/fraction, we multiply both sides of the equation by 4: 4f - 4f/4 = 30 *4 4f - f = 120 3f = 120 To solve for f, we divide each side of the equation by 3: 3f/3 = 120/3 Cancel the 3's on the left side and we get: f = [B]40[/B]
A square has a perimeter of 24 inches. What is the area of the square?
A square has a perimeter of 24 inches. What is the area of the square? Perimeter of a square = 4s where s = the length of a side. Therefore, we have: 4s = P 4s = 24 Using our equation solver, [URL='https://www.mathcelebrity.com/1unk.php?num=4s%3D24&pl=Solve']we type in 4s = 24[/URL] and get: s = 6 The problems asks for area of a square. It's given by A = s^2 Plugging in s = 6, we get: A = 6^2 A = 6 * 6 A = [B]36 [/B] Now if you want a shortcut in the future, type in the shape and measurement you know. Such as: [I][URL='https://www.mathcelebrity.com/square.php?num=24&pl=Perimeter&type=perimeter&show_All=1']square perimeter = 24[/URL][/I] From the link, you'll learn every other measurement about the square.
a stone mason builds 7 houses in 3 days. How many days does it take to build 11 houses?
a stone mason builds 7 houses in 3 days. How many days does it take to build 11 houses? The build rate of houses per days is proportional. Set up a proportion of [I]houses to days[/I] where d is the number of days it takes to build 11 houses: 7/3 = 11/d Cross multiply: Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2 7d = 11 * 3 7d = 33 Divide each side of the equation by 7: 7d/7 = 33/7 d = [B]4.7142857142857[/B]
A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is
A storage box has a volume of 56 cubic inches. The base of the box is 4 inches by 4 inches. What is the height of the box? The volume of the box is l x w x h. We're given l and w = 4. So we want height: 56 = 4 x 4 x h 16h = 56 [URL='https://www.mathcelebrity.com/1unk.php?num=16h%3D56&pl=Solve']Type this equation into our search engine[/URL] and we get: h = [B]3.5[/B]
A store is offering a 11% discount on all items. Write an equation relating the final price
A store is offering a 11% discount on all items. Write an equation relating the final price 11% discount means we pay 100% - 11% = 89% of the full price. Since 89% as a decimal is 0.89. With a final price f and an original price p, we have: [B]F = 0.89p[/B]
A store is offering a 15% discount on all items. Write an equation relating the sale price S for an
A store is offering a 15% discount on all items. Write an equation relating the sale price S for an item to its list price L If we give a discount of 15%, then we pay 100% - 15% = 85% of the list price. 85% as a decimal is 0.85, So we have: L = 0.85S
A store is offering a 18% discount on all items. Write an equation relating the sale price S for an
A store is offering a 18% discount on all items. Write an equation relating the sale price S for an item to its list price L. 18% discount means we subtract 18% (0.18) as a decimal, from the 100% of the price: S = L(1 - 0.18) [B]S = 0.82L[/B]
A store sells small notebooks for $6 and large notebooks for $12. If a student buys 6 notebooks and
A store sells small notebooks for $6 and large notebooks for $12. If a student buys 6 notebooks and spends $60, how many of each did he buy? Let the amount of small notebooks be s. Let the amount of large notebooks be l. We're given two equations: [LIST=1] [*]l + s = 6 [*]12l + 6s = 60 [/LIST] Multiply equation (1) by -6 [LIST=1] [*]-6l - 6s = -36 [*]12l + 6s = 60 [/LIST] Now add equation 1 to equation 2: 12l - 6l + 6s - 6s = 60 - 36 Cancel the 6s terms, and we get: 6l = 24 To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=6l%3D24&pl=Solve']type this equation into our search engine[/URL] and we get: l = [B]4 [/B] Now substitute this into equation 1: 4 + s = 6 To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=4%2Bs%3D6&pl=Solve']we type this equation into our search engine[/URL] and we get: s = [B]2[/B]
A straight line has the equation ax + by=23. The points (5,-2) and (1,-5) lie on the line. Find the
A straight line has the equation ax + by=23. The points (5,-2) and (1,-5) lie on the line. Find the values of a and b. plug in both points and form 2 equations: [LIST=1] [*]5a - 2b = 23 [*]1x - 5b = 23 [/LIST] We can solve this simultaneous equations any one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=5a+-+2b+%3D+23&term2=1a+-+5b+%3D+23&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]a = 3[/B] [*][B]b = -4[/B] [/LIST]
A student and the marine biologist are together at t = 0. The student ascends more slowly than the m
A student and the marine biologist are together at t = 0. The student ascends more slowly than the marine biologist. Write an equation of a function that could represent the student's ascent. Please keep in mind the slope for the marine biologist is 12. Slope means rise over run. In this case, rise is the ascent distance and run is the time. 12 = 12/1, so for each second of time, the marine biologist ascends 12 units of distance If the student ascends slower, than the total distance gets reduced by an unknown factor, let's call it c. So we have the student's ascent function as: [B]y(t) = 12t - c[/B]
a student has $50 in saving and earns $40 per week. How long would it take them to save $450
a student has $50 in saving and earns $40 per week. How long would it take them to save $450 Set up the savings function S(w), where w is the number of weeks. The balance, S(w) is: S(w) = Savings Per week * w + Initial Savings S(w) = 40w + 50 The problems asks for how many weeks for S(w) = 450. So we have; 40w + 50 = 450 To solve for w, we[URL='https://www.mathcelebrity.com/1unk.php?num=40w%2B50%3D450&pl=Solve'] type this equation in our search engine[/URL] and we get: w = [B]10[/B]
A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a.
A sum of money doubles in 20 years on simple interest. It will get triple at the same rate in: a. 40 years b. 50 years c. 30 years d. 60 years e. 80 years Simple interest formula if we start with 1 dollar and double to 2 dollars: 1(1 + i(20)) = 2 1 + 20i = 2 Subtract 1 from each side: 20i = 1 Divide each side by 20 i = 0.05 Now setup the same simple interest equation, but instead of 2, we use 3: 1(1 + 0.05(t)) = 3 1 + 0.05t = 3 Subtract 1 from each side: 0.05t = 2 Divide each side by 0.05 [B]t = 40 years[/B]
A super deadly strain of bacteria is causing the zombie population to double every day. Currently, t
A super deadly strain of bacteria is causing the zombie population to double every day. Currently, there are 25 zombies. After how many days will there be over 25,000 zombies? We set up our exponential function where n is the number of days after today: Z(n) = 25 * 2^n We want to know n where Z(n) = 25,000. 25 * 2^n = 25,000 Divide each side of the equation by 25, to isolate 2^n: 25 * 2^n / 25 = 25,000 / 25 The 25's cancel on the left side, so we have: 2^n = 1,000 Take the natural log of each side to isolate n: Ln(2^n) = Ln(1000) There exists a logarithmic identity which states: Ln(a^n) = n * Ln(a). In this case, a = 2, so we have: n * Ln(2) = Ln(1,000) 0.69315n = 6.9077 [URL='https://www.mathcelebrity.com/1unk.php?num=0.69315n%3D6.9077&pl=Solve']Type this equation into our search engine[/URL], we get: [B]n = 9.9657 days ~ 10 days[/B]
A survey of 950 college students found that 85% of the men and 90% of the women identified math as t
A survey of 950 college students found that 85% of the men and 90% of the women identified math as their favorite subject. If altogether 834 students reported math to be their favorite subject how many men and women participated in the survey Let m be the number of men and w be the number of women. We are given 2 equations [LIST=1] [*]m + w = 950 [*]0.85m + 0.90w = 834 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+w+%3D+950&term2=0.85m+%2B+0.90w+%3D+834&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [LIST] [*]m = [B]420[/B] [*]w = [B]530[/B] [/LIST]
A sweater costs $40. That is 5 times as much as a shirt. What is the price of the shirt?
A sweater costs $40. That is 5 times as much as a shirt. What is the price of the shirt? State this as an equation. Let the price of the shirt be s. 5 times as much means we multiply s by 5: 5s = 40 [URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D40&pl=Solve']Type this equation into the search engine[/URL], we get: s = [B]8[/B]
A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take
A tank has 800 liters of water. 12ml of water leaks from the tank every second.how long does it take for the tank to be empty Assumptions and givens: [LIST] [*]Let the number of seconds be s. [*]An empty tank means 0 liters of water. [*]Leaks mean we subtract from the starting volume. [/LIST] We have the following relation: 800 - 12s = 0 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=800-12s%3D0&pl=Solve']type it in our search engine[/URL] and we get: s = 66.67 seconds
A taxi cab in Chicago charges $3 per mile and $1 for every person. If the taxi cab ride for two peop
A taxi cab in Chicago charges $3 per mile and $1 for every person. If the taxi cab ride for two people costs $20. How far did the taxi cab travel. Set up a cost function C(m) where m is the number of miles driven: C(m) = cost per mile * m + per person fee [U]Calculate per person fee:[/U] per person fee = $1 per person * 2 people per person fee = $2 [U]With a cost per mile of $3 and per person fee of $2, we have:[/U] C(m) = cost per mile * m + per person fee C(m) = 3m + 2 The problem asks for m when C(m) = 20, so we set 3m + 2 equal to 20: 3m + 2 = 20 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%2B2%3D20&pl=Solve']plug it in our search engine[/URL] and we get: m = [B]6[/B]
A taxi cab in nyc charges a pick up fee of $5.00 . The customer must also pay $2.59 for each mile th
A taxi cab in nyc charges a pick up fee of $5.00 . The customer must also pay $2.59 for each mile that the taxi must drive to reach their destination. Write an equation Set up a cost function C(m) where m is the number of miles: C(m) = Mileage Charge * m + pick up fee [B]C(m) = 2.59m + 5[/B]
A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to s
A taxi charges a flat rate of $1.50 with an additional charge of $0.80 per mile. Samantha wants to spend less than $12 on a ride. Which inequality can be used to find the distance Samantha can travel? Set up the travel cost equation where m is the number of miles: C(m) = 0.8m + 1.50 If Samantha wants to spend less than 12 per ride, we have an inequality where C(m) < 12: [B]0.8m + 1.50 < 12[/B]
A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to
A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most $10 to spend on the cab ride, how far could she travel? Set up a cost function C(m), where m is the number of miles: C(m) = Cost per mile * m + flat rate C(m) = 0.65m + 1.75 The problem asks for m when C(m) = 10 0.65m + 1.75 = 10 [URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get: m = [B]12.692 miles[/B]
A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to
A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel Set up a cost function C(m), where m is the number of miles Erica can travel. We have: C(m) = 0.65m + 1.75 If C(m) = 10, we have: 0.65m + 1.75 = 10 [URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into our search engine[/URL], we get: m = 12.69 miles If the problem asks for complete miles, we round down to 12 miles.
A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to
A taxi charges a flat rate of $1.75, plus an additional $0.65 per mile. If Erica has at most 10$ to spend on the cab ride, how far could she travel? Set up the cost function C(m) where m is the number of miles: C(m) = 0.65m + 1.75 If Erica has $10, then C(m) = 10, so we have: 0.65m + 1.75 = 10 [URL='https://www.mathcelebrity.com/1unk.php?num=0.65m%2B1.75%3D10&pl=Solve']Typing this equation into the search engine[/URL], we get m = 12.69 if the answer asks for whole number, then we round down to m = 12
A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spe
A taxi charges a flat rate of 1.75, plus an additional 0.65 per mile. If Erica has at most 10 to spend on the cab ride, how far could she travel? Setup an equation where x is the number of miles traveled: 0.65x + 1.75 = 10 Subtract 1.75 from each side: 0.65x = 8.25 Divide each side by 0.65 [B]x = 12.69 miles[/B] If we do full miles, we round down to 12.
A taxi service charges an initial fee of $3 plus $1.80 per mile. How far can you travel for $12?
A taxi service charges an initial fee of $3 plus $1.80 per mile. How far can you travel for $12? Given m for miles, we have the equation: 1.80m + 3 = 12 We [URL='https://www.mathcelebrity.com/1unk.php?num=1.80m%2B3%3D12&pl=Solve']type this equation into our search engine[/URL] to solve for m and we get: m = [B]5[/B]
A teacher�s salary was $3300 after she had received an increase of 10%. Calculate the teacher�s sala
A teacher�s salary was $3300 after she had received an increase of 10%. Calculate the teacher�s salary if she has received an increase of 20% instead. First, we need to find the starting salary. Let the starting salary be s. Since 10% as a decimal is 0.10, We're given: s*(1.10) = 3300 1.10s = 3300 To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=1.10s%3D3300&pl=Solve']we type this equation into our search engine[/URL] and we get: s = [B]3000[/B] The problem asks for the new salary if the teacher's starting salary was increased by 20%. 20% as a decimal is 0.20, so we have: 3000(1.2) = $[B]3,600[/B]
A test has twenty questions worth 100 points . The test consist of true/false questions worth 3 poin
A test has twenty questions worth 100 points . The test consist of true/false questions worth 3 points each and multiple choice questions worth 11 points each . How many multiple choice questions are on the test? Set up equations where t = true false and m = multiple choice: [LIST=1] [*]t + m = 20 [*]3t + 11m = 100 [/LIST] Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=t+%2B+m+%3D+20&term2=3t+%2B+11m+%3D+100&pl=Cramers+Method']simultaneous equation calculator[/URL]: [B]t = 15, m = 5[/B]
A test has twenty questions worth 100 points total. the test consists of true/false questions worth
A test has twenty questions worth 100 points total. the test consists of true/false questions worth 3 points each and multiple choice questions worth 11 points each. How many true/false questions are on the test? Let m be the number of multiple choice questions and t be the number of true/false questions. We're given: [LIST=1] [*]m + t = 20 [*]11m + 3t = 100 [/LIST] We can solve this system of equations 3 ways below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the following answers: [LIST] [*][B]m = 5[/B] [*][B]t = 15[/B] [/LIST] Check our work in equation 1: 5 + 15 ? 20 [I]20 = 20[/I] Check our work in equation 2: 11(5) + 3(15) ? 100 55 + 45 ? 100 [I]100 = 100[/I]
A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 poin
A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test? Let the number of true/false questions be t. Let the number of multiple choice questions be m. We're given two equations: [LIST=1] [*]m + t = 20 [*]11m + 3t = 100 [/LIST] We have a set of simultaneous equations. We can solve this using 3 methods: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1m+%2B+t+%3D+20&term2=11m+%2B+3t+%3D+100&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we pick, we get the same answer: [LIST] [*][B]m = 5[/B] [*][B]t = 15[/B] [/LIST]
a textbook store sold a combined total of 296 sociology and history text books in a week. the number
a textbook store sold a combined total of 296 sociology and history text books in a week. the number of history textbooks sold was 42 less than the number of sociology textbooks sold. how many text books of each type were sold? Let h = history book and s = sociology books. We have 2 equations: (1) h = s - 42 (2) h + s = 296 Substitute (1) to (2) s - 42 + s = 296 Combine variables 2s - 42 = 296 Add 42 to each side 2s = 338 Divide each side by 2 s = 169 So h = 169 - 42 = 127
A textbook store sold a combined total of 307 biology and chemistry textbooks in a week. The number
A textbook store sold a combined total of 307 biology and chemistry textbooks in a week. The number of chemistry textbooks sold was 71 less than the number of biology textbooks sold. How many textbooks of each type were sold? Let b be the number of biology books and c be the number of chemistry books. We have two equations: [LIST=1] [*]b + c = 307 [*]c = b - 71 [/LIST] Substitute (2) into (1) for c b + (b - 71) = 307 Combine like terms: 2b - 71 = 307 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2b-71%3D307&pl=Solve']equation solver[/URL], we get: [B]b = 189[/B] Now substitute that into (2): c = 189 - 71 [B]c = 118[/B]
A theater has 1200 seats. Each row has 20 seats. Write and solve an equation to find the number x of
A theater has 1200 seats. Each row has 20 seats. Write and solve an equation to find the number x of rows in the theater. Let x be the number of rows in the theater: x = Total Seats / Seats per row x = 1200/20 x = [B]60[/B]
A theater is 3/4 full. When 96 people leave, the theater is only 35% full. How many seat are there
A theater is 3/4 full. When 96 people leave, the theater is only 35% full. How many seats are there? Let the full capacity of seats in the theater be s. We're given: 3/4s - 96 = 0.35s (Since 35% is 0.35) We also know that 3/4 = 0.75, so let's use this to have decimals: 0.75s - 96 = 0.35s To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75s-96%3D0.35s&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]240[/B]
A theatre contains 459 seats and the ticket prices for a recent play were $53 for adults and $16 for
A theatre contains 459 seats and the ticket prices for a recent play were $53 for adults and $16 for children. If the total proceeds were $13,930 for a sold- out matinee, how many of each type of ticket were sold? Let a be the number of adult tickets and c be the number of children tickets. We have the following equations: [LIST=1] [*]a + c =459 [*]53a + 16c = 13930 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a%2Bc%3D459&term2=53a+%2B+16c+%3D+13930&pl=Cramers+Method']simultaneous equation calculator[/URL], we have: [B]a = 178 c = 281[/B]
A tire repair shop charges $5 for tool cost and $2 for every minute the worker spends on the repair.
A tire repair shop charges $5 for tool cost and $2 for every minute the worker spends on the repair. A) Write an equation of the total cost of repair, $y, in terms of a total of x minutes of repair. y = Variable Cost + Fixed Cost y = Cost per minute of repair * minutes of repair + Tool Cost [B]y = 2x + 5[/B]
A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For
A tortoise is walking in the desert. It walks at a speed of 5 meters per minute for 12.5 meters. For how many minutes does it walk? Distance formula (d) for a rate (r) and time (t) is: d = rt We're given d = 12.5 and r = 5 12.5 = 5t 5t = 12.5 Solve for t. Divide each side of the equation by 5: 5t/5 = 12.5/5 Cancel the 5's on left side and we get: t = [B]2.5[/B]
A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was
A tow truck charges a service fee of $50 and an additional fee of $1.75 per mile. What distance was Marcos car towed if he received a bill for $71 Set up a cost equation C(m) where m is the number of miles: C(m) = Cost per mile * m + Service Fee Plugging in the service fee of 50 and cost per mile of 1.75, we get: C(m) = 1.75m + 50 The question asks for what m is C(m) = 71. So we set C(m) = 71 and solve for m: 1.75m + 50 = 71 Solve for [I]m[/I] in the equation 1.75m + 50 = 71 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 50 and 71. To do that, we subtract 50 from both sides 1.75m + 50 - 50 = 71 - 50 [SIZE=5][B]Step 2: Cancel 50 on the left side:[/B][/SIZE] 1.75m = 21 [SIZE=5][B]Step 3: Divide each side of the equation by 1.75[/B][/SIZE] 1.75m/1.75 = 21/1.75 m = [B]12[/B]
A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. T
A toy company makes "Teddy Bears". The company spends $1500 for factory expenses plus $8 per bear. The company sells each bear for $12.00 each. How many bears must this company sell in order to break even? [U]Set up the cost function C(b) where b is the number of bears:[/U] C(b) = Cost per bear * b + factory expenses C(b) = 8b + 1500 [U]Set up the revenue function R(b) where b is the number of bears:[/U] R(b) = Sale Price per bear * b R(b) = 12b [U]Break-even is where cost equals revenue, so we set C(b) equal to R(b) and solve for b:[/U] C(b) = R(b) 8b + 1500 = 12b To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=8b%2B1500%3D12b&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]375[/B]
A train leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3
A train leaves San Diego at 1:00 PM. A second train leaves the same city in the same direction at 3:00 PM. The second train travels 30mph faster than the first. If the second train overtakes the first at 6:00 PM, what is the speed of each of the two trains? Distance = Rate x Time Train 1: d = rt t = 1:oo PM to 6:00 PM = 5 hours So we have d = 5r Train 2: d = (r + 30)t t = 3:oo PM to 6:00 PM = 3 hours So we have d = 3(r + 30) Set both distances equal to each other since overtake means Train 2 caught up with Train 1, meaning they both traveled the same distance: 5r = 3(r + 30) Multiply through: 3r + 90 = 5r [URL='https://www.mathcelebrity.com/1unk.php?num=3r%2B90%3D5r&pl=Solve']Run this equation through our search engine[/URL], and we get [B]r = 45[/B]. This is Train 1's Speed. Train 2's speed = 3(r + 30). Plugging r = 45 into this, we get 3(45 + 30). 3(75) [B]225[/B]
A traveler is walking on a moving walkway in an airport. the traveler must walk back on the walkway
A traveler is walking on a moving walkway in an airport. the traveler must walk back on the walkway to get a bag he forgot. the traveler's ground speed is 2 ft/s against the walkway and 6 ft/s with the walkway. what is the traveler's speed off the walkway? What is the speed of the moving walkway. We have two equations, where w is the speed of the walkway and t is the speed of the traveler. [LIST=1] [*]t - w = 2 [*]t + w = 6 [*]Rearrange (1) to solve for t: t = w + 2 [/LIST] Now plug (3) into (2) (w + 2) + w = 6 Combine like terms: 2w + 2 = 6 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B2%3D6&pl=Solve']equation solver[/URL], we get [B]w = 2[/B] Plug this into (1) t - 2 = 2 Add 2 to each side [B]t = 4[/B]
A used book store also started selling used CDs and videos. In the first week, the store sold a comb
A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold Let c be the number of CDs sold, and v be the number of videos sold. We're given 2 equations: [LIST=1] [*]c + v = 40 [*]4c + 6v = 180 [/LIST] You can solve this system of equations three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter what method we choose, we get [B]c = 30, v = 10[/B]. Now let's check our work for both given equations for c = 30 and v = 10: [LIST=1] [*]30 + 10 = 40 <-- This checks out [*]4c + 6v = 180 --> 4(30) + 6(10) --> 120 + 60 = 180 <-- This checks out [/LIST]
A used book store also started selling used CDs and videos. In the first week, the store sold a comb
A used book store also started selling used CDs and videos. In the first week, the store sold a combination of 40 CDs and videos. They charged $4 per CD and $6 per video and the total sales were $180. Determine the total number of CDs and videos sold. Let the number of cd's be c and number of videos be v. We're given two equations: [LIST=1] [*]c + v = 40 [*]4c + 6v = 180 [/LIST] We can solve this system of equations using 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+v+%3D+40&term2=4c+%2B+6v+%3D+180&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [B]c = 30 v = 10[/B]
A vehicle purchased for $25,000 depreciates at a constant rate of 5%. Determine the approximate valu
A vehicle purchased for $25,000 depreciates at a constant rate of 5%. Determine the approximate value of the vehicle 11 years after purchase. Round to the nearest whole dollar. Depreciation at 5% means it retains 95% of the value. Set up the depreciation equation to get Book Value B(t) at time t. B(t) = $25,000 * (1 - 0.05)^t Simplifying, this is: B(t) = $25,000 * (0.95)^t The problem asks for B(11) B(11) = $25,000 * (0.95)^11 B(11) = $25,000 * 0.5688 B(11) = [B]$14,220[/B]
A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor
A vendor sells h hot dogs and s sodas. If a hot dog costs twice as much as a soda, and if the vendor takes in a total of d dollars, how many cents does a soda cost? Let the cost of the soda be p. So the cost of a hot dog is 2p. The total cost of hot dogs: 2hp The total cost of sodas: ps The total cost of both equals d. So we set the total cost of hots dogs plus sodas equal to d: 2hp + ps = d We want to know the cost of a soda (p). So we have a literal equation. We factor out p from the left side: p(2h + s) = d Divide each side of the equation by (2h + s) p(2h + s)/(2h + s) = d/(2h + s) Cancel the (2h + s) on the left side, we get: p = [B]d/(2h + s[/B])
A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $
A video store charges a monthly membership fee of $7.50, but the charge to rent each movie is only $1.00 per movie. Another store has no membership fee, but it costs $2.50 to rent each movie. How many movies need to be rented each month for the total fees to be the same from either company? Set up a cost function C(m) where m is the number of movies you rent: C(m) = Rental cost per movie * m + Membership Fee [U]Video Store 1 cost function[/U] C(m) = 1m + 7.5 Video Store 2 cost function: C(m) = 2.50m We want to know when the costs are the same. So we set each C(m) equal to each other: m + 7.5 = 2.50m To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B7.5%3D2.50m&pl=Solve']we type it in our search engine[/URL] and we get: m = [B]5[/B]
A virus is spreading exponentially. The initial amount of people infected is 40 and is increasing at
A virus is spreading exponentially. The initial amount of people infected is 40 and is increasing at a rate of 5% per day. How many people will be infected with the virus after 12 days? We have an exponential growth equation below V(d) where d is the amount of days, g is the growth percentage, and V(0) is the initial infected people: V(d) = V(0) * (1 + g/100)^d Plugging in our numbers, we get: V(12) = 40 * (1 + 5/100)^12 V(12) = 40 * 1.05^12 V(12) = 40 * 1.79585632602 V(12) = 71.8342530409 or [B]71[/B]
A washer and a dryer cost 600 combined. The cost of the washer is 3 times the cost of the dryer. Wha
A washer and a dryer cost 600 combined. The cost of the washer is 3 times the cost of the dryer. What is the cost of the dryer? Let w be the cost of the washer. Let d be the cost of the dryer. We have 2 given equations: [LIST=1] [*]w + d = 600 [*]w = 3d [/LIST] Substitute (2) into (1) (3d) + d = 600 4d = 600 [URL='http://www.mathcelebrity.com/1unk.php?num=4d%3D600&pl=Solve']Run it through our equation calculator[/URL], to get [B]d = 150[/B].
A water tank holds 236 gallons but is leaking at a rate of 3 gallons per week. A second water tank h
A water tank holds 236 gallons but is leaking at a rate of 3 gallons per week. A second water tank holds 354 gallons but is leaking at a rate if 5 gallons per week. After how many weeks will the amount of water in the two tanks be the same Let w be the number of weeks of leaking. We're given two Leak equations L(w): [LIST=1] [*]L(w) = 236 - 3w [*]L(w) = 354 - 5w [/LIST] When the water in both tanks is the same, we can set both L(w) equations equal to each other: 236 - 3w = 354 - 5w To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=236-3w%3D354-5w&pl=Solve']type it in our search engine[/URL] and we get: w = [B]59[/B]
A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages?
A woman is one-half as old as her mother. The sum of their ages is 75. What are their ages? Let the woman's age be w. Let the mother's age be m. We're given two equations: [LIST=1] [*]w = m/2 [*]m + w = 75 [/LIST] Substitute equation (1) into equation (2) for w: m + m/2 = 75 To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%2F2%3D75&pl=Solve']type this equation into our search engine [/URL]and we get: m = [B]50 [/B] To solve for w, we plug m = 50 into equation (1): w = 50/2 w = [B]25[/B]
A yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost
A yoga member ship costs $16 and additional $7 per class. Write a linear equation modeling the cost of a yoga membership? Set up the cost function M(c) for classes (c) [B]M(c) = 16 + 7c[/B]
A zoo has 15 Emperor penguins. The Emperor penguins make up 30% percent of all the penguins at the z
A zoo has 15 Emperor penguins. The Emperor penguins make up 30% percent of all the penguins at the zoo. How many penguins live at the zoo? Let p be the total number penguins at the zoo. We're told: 30% of p = 15 Since 30% = 0.3, we have: 0.3p = 15 Solve for [I]p[/I] in the equation 0.3p = 15 [SIZE=5][B]Step 1: Divide each side of the equation by 0.3[/B][/SIZE] 0.3p/0.3 = 15/0.3 p = [B]50[/B]
A+B+D=255 B+15=A D+12=B A=
A+B+D=255 B+15=A D+12=B A= [LIST=1] [*]A + B + D = 255 [*]B + 15 = A [*]D + 12 = B [*]A = ? [*]Rearrange (3) to solve for D by subtracting 12 from each side: D = B - 12 [/LIST] Substitute (2) and (5) into 1 (B + 15) + B + (B - 12) = 255 Combine like terms: 3B + 3 = 255 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3b%2B3%3D255&pl=Solve']equation solver[/URL], b = 84 Substitute b = 84 into equation (2): A = 84 + 15 [B]A = 99[/B]
Aaron bought a bagel and 3 muffins for $7.25. Bea bought a bagel and 2 muffins for $6. How much is b
Aaron bought a bagel and 3 muffins for $7.25. Bea bought a bagel and 2 muffins for $6. How much is bagel and how much is a muffin? Let b be the number of bagels and m be the number of muffins. We have two equations: [LIST=1] [*]b + 3m = 7.25 [*]b + 2m = 6 [/LIST] Subtract (2) from (1) [B]m = 1.25 [/B] Plug this into (2), we have: b + 2(1.25) = 6 b + 2.5 = 6 Subtract 2.5 from each side [B]b = 3.5[/B]
ab/d + c = e for d
ab/d + c = e for d I know this is a literal equation because we are asked to solve for a variable [U]in terms of[I] another variable [/I][/U] Subtract c from each side to isolate the d term: ab/d + c - c = e - c Cancel the c's on the left side and we get: ab/d = e - c Cross multiply: ab = d(e - c) Divide each side of the equation by (e - c): ab/(e - c)= d(e - c)/(e - c) Cancel the (e - c) on the right side, and we get: d = [B]ab/(e - c)[/B]
Acceleration
Solves for any of the 4 items in the acceleration equation including initial velocity, velocity, and time.
According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eatin
According to the American Bureau of Labor Statistics, you will devote 32 years to sleeping and eating. The number of years sleeping will exceed the number of years eating by 24. Over your lifetime, how many years will you spend on each of these activities? Assumptions: [LIST] [*]Let years eating be e [*]Let years sleeping be s [/LIST] We're given: [LIST=1] [*]s = e + 24 [*]e + s = 32 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for s: e + e + 24 = 32 To solve this equation for e, we [URL='https://www.mathcelebrity.com/1unk.php?num=e%2Be%2B24%3D32&pl=Solve']type it in our math engine[/URL] and we get: e = [B]4 [/B] Now, we take e = 4 and substitute it into equation (1) to solve for s: s = 4 + 24 s = [B]28[/B]
acw+cz=y for a
acw+cz=y for a Solve this literal equation: Subtract cz from each side: acw + cz - cz = y - cz Cancel the cz on the left side: acw = y - cz Divide each side by cw to isolate a: acw/cw = (y - cz)/cw Cancel cw on the left side: [B]a = (y - cz)/cw[/B]
Admir works at a coffee shop and earns $9/hour he also works at a grocery store and earns $15/hour.
Admir works at a coffee shop and earns $9/hour he also works at a grocery store and earns $15/hour. Last week he earned $500 dollars. Write an equation that represents the situation. [LIST] [*]Let c be the hours Admir works at the coffee shop. [*]Let g be the hours Admir works at the grocery store. [/LIST] Since earnings equal hourly rate times hours, We have the following equation: [B]9c + 15g = 500[/B]
Admission to a baseball game is $2.00 for general admission and $5.50 for reserved seats. The recei
Admission to a baseball game is $2.00 for general admission and $5.50 for reserved seats. The receipts were $3577.00 for 1197 paid admissions. How many of each ticket were sold? Let g be the number of tickets for general admission Let r be the number of tickets for reserved seats We have two equations: [LIST=1] [*]g + r = 1197 [*]2g + 5.50r = 3577 [/LIST] We can solve this a few ways, but let's use substitution using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=g+%2B+r+%3D+1197&term2=2g+%2B+5.50r+%3D+3577&pl=Substitution']simultaneous equations calculator[/URL]: [LIST] [*][B]r = 338[/B] [*][B]g = 859[/B] [/LIST]
admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were col
admission to the school fair is $2.50 for students and $3.75 for others. if 2848 admissions were collected for a total of 10,078.75, how many students attended the fair Let the number of students be s and the others be o. We're given two equations: [LIST=1] [*]o + s = 2848 [*]3.75o + 2.50s = 10078.75 [/LIST] Since we have no coefficients for equation 1, let's solve this the fast way using substitution. Rearrange equation 1 by subtracting o from each side to isolate s [LIST=1] [*]o = 2848 - s [*]3.75o + 2.50s = 10078.75 [/LIST] Now substitute equation 1 into equation 2: 3.75(2848 - s) + 2.50s =10078.75 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=3.75%282848-s%29%2B2.50s%3D10078.75&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]481[/B]
After 5 years, a car is worth $22,000. It�s value decreases by $1,500 a year, which of the following
After 5 years, a car is worth $22,000. It�s value decreases by $1,500 a year, which of the following equations could represent this situation? Group of answer choices Let y be the number of years since 5 years. Our Book value B(y) is: [B]B(y) = 22,000 - 1500y[/B]
after buying some tickets for $19.00, Ann has $18.00 left. How much money did Ann have to beginwith
After buying some tickets for $19.00, Ann has $18.00 left. How much money did Ann have to begin with? Let the beginning amount be b. We're given: b - 19 = 18. <-- [I]We subtract 19 because a purchase is a spend reducing the original amount[/I] To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b-19%3D18&pl=Solve']type the equation b - 19 = 18 into our search engine [/URL]and we get: b = [B]37[/B]
Age now and then
I brute forced this and got a wrong answer, logic tells me is right. I tried the calculator here but maybe messed up the equation using another users problem as an example. Having no luck. Problem: Jacob is 4 times the age of Clinton. 8 years ago Jacob was 9 times the age of Clinton. How old are they now and how old were they 8 years ago?
Age now and then
Let j be Jacob's age and c be Clinton's age. We have: [LIST=1] [*]j = 4c [*]j - 8 = 9(4c - 8) [/LIST] Substitute (1) into (2) (4c) - 8 = 36c - 72 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D36c-72&pl=Solve']equation solver,[/URL] we get c = 2 Which means j = 4(2) = 8 8 years ago, Jacob was just born. Which means Clinton wasn't even born yet.
Age now and then
she wrote it down wrong! The 9 should have been a 10. So I tried 4c-8=40c-80 in the equation solver and it also came back with C=2 which was the same answer you got before?
Age now and then
she wrote it down wrong! The 9 should have been a 10. So I tried 4c-8=40c-80 in the equation solver and it also came back with C=2 which was the same answer you got before? [QUOTE="Drew, post: 1161, member: 63"]she wrote it down wrong! The 9 should have been a 10. So I tried 4c-8=40c-80 in the equation solver and it also came back with C=2 which was the same answer you got before?[/QUOTE] oh and my brute force answer was 12-48 and 8 years earlier was 4-40
Age now and then
I read it wrong before. Here you go: Jacob is 4 times the age of Clinton. 8 years ago Jacob was 10 times the age of Clinton. How old are they now and how old were they 8 years ago? [LIST=1] [*]j = 4c [*]j - 8 = 10(c - 8) [/LIST] Substitute (1) into (2) (4c) - 8 = 10c - 80 [URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D10c-80&pl=Solve']Equation solver[/URL] gives us [B]c = 12[/B] which means j = 4(12) = [B]48[/B]. 8 years ago,[B] j = 40 and c = 4[/B] which holds the 10x rule.
Age now and then
[QUOTE="math_celebrity, post: 1163, member: 1"]I read it wrong before. Here you go: Jacob is 4 times the age of Clinton. 8 years ago Jacob was 10 times the age of Clinton. How old are they now and how old were they 8 years ago? [LIST=1] [*]j = 4c [*]j - 8 = 10(c - 8) [/LIST] Substitute (1) into (2) (4c) - 8 = 10c - 80 [URL='http://www.mathcelebrity.com/1unk.php?num=4c-8%3D10c-80&pl=Solve']Equation solver[/URL] gives us [B]c = 12[/B] which means j = 4(12) = [B]48[/B]. 8 years ago,[B] j = 40 and c = 4[/B] which holds the 10x rule.[/QUOTE] Thank you, I see what I did wrong!
Age now problems
Age of the older boy is o, younger boy is y. We have the following equations: [LIST=1] [*]o = 2y [*]o - 5 = 3(y - 5) [/LIST] Plug (1) into (2) (2y) - 5 = 3y - 15 Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=2y-5%3D3y-15&pl=Solve']equation solver[/URL], we get: [B]y = 10[/B] Plug that into (1), we get: o = 2(10), [B]o = 20[/B]
Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total v
Ahmad has a jar containing only 5-cent and 20-cent coins. In total there are 31 coins with a total value of $3.50. How many of each type of coin does Ahmad have? Let the number of 5-cent coins be f. Let the number of 20-cent coins be t. We're given two equations: [LIST=1] [*]f + t = 31 [*]0.05f + 0.2t = 3.50 [/LIST] We can solve this simultaneous system of equations 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+31&term2=0.05f+%2B+0.2t+%3D+3.50&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter which method we choose, we get: [LIST] [*][B]f = 18[/B] [*][B]t = 13[/B] [/LIST]
Al's Rentals charges $25 per hour to rent a sailboard and a wetsuit. Wendy's Rentals charges $20 per
Al's Rentals charges $25 per hour to rent a sailboard and a wetsuit. Wendy's Rentals charges $20 per hour plus $15 extra for a wetsuit. Find the number of hours for which the total charges for both companies would be the same. Al's Rentals Cost Equation C(h) where h is the number of hours you rent a sailboard and wetsuit: C(h) = 25h Wendy's Rentals Cost Equation C(h) where h is the number of hours you rent a sailboard and wetsuit: C(h) = 20h + 15 We want to set both cost equation equal to each other, and solve for h: 20h + 15 = 25h [URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B15%3D25h&pl=Solve']Typing this equation into our search engine[/URL], we get: h = [B]3[/B]
Alberto and Willie each improved their yards by planting daylilies and ivy. They bought their suppli
Alberto and Willie each improved their yards by planting daylilies and ivy. They bought their supplies from the same store. Alberto spent $64 on 3 daylilies and 8 pots of ivy. Willie spent $107 on 9 daylilies and 7 pots of ivy. What is the cost of one daylily and the cost of one pot of ivy? Assumptions: [LIST] [*]Let d be the cost of one daylily [*]Let i be the cost of one pot of ivy [/LIST] Givens: [LIST=1] [*]3d + 8i = 64 [*]9d + 7i = 107 [/LIST] To solve this system of equations, you can use any of three methods below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3d+%2B+8i+%3D+64&term2=9d+%2B+7i+%3D+107&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3d+%2B+8i+%3D+64&term2=9d+%2B+7i+%3D+107&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3d+%2B+8i+%3D+64&term2=9d+%2B+7i+%3D+107&pl=Cramers+Method']Cramer's Method[/URL] [/LIST] No matter what method we use, we get the same answer: [LIST] [*][B]d = 8[/B] [*][B]i = 5[/B] [/LIST] [B][MEDIA=youtube]K1n3niERg-U[/MEDIA][/B]
Alberto�s salary was $1500 greater than 5 times Nick�s salary. Write an equation stating Alberto�s a
Alberto�s salary was $1500 greater than 5 times Nick�s salary. Write an equation stating Alberto�s and Nick�s salaries in terms of x and y. Let x be Alberto's salary. Let y be Nick's salary. We have: Let's break this down: [LIST=1] [*]5 times Nick's salary (y), means we multiply the variable y by 5 [*]$1500 greater means we add $1500 to 5y [/LIST] [B]x = 5y - 1500[/B]
Alberto�s salary was $2000 greater than 4 times Nick�s salary. Write an equation stating Alberto�s a
Alberto�s salary was $2000 greater than 4 times Nick�s salary. Write an equation stating Alberto�s and Nick�s salaries in terms of x and y. If Alberto's salary is x and Nick's salary is y, we have: [B]x = 4y + 2000[/B]
Alberto�s salary was $2000 greater than 4 times Nick�s salary. Write an equation stating Alberto�s a
Alberto�s salary was $2000 greater than 4 times Nick�s salary. Write an equation stating Alberto�s and Nick�s salaries in terms of x and y. Let Alberto's salary be x, and Nick's salary be y. We have: [B]x = 4y + 2000[/B]
Alberto�s salary was $2000 greater than 4 times Nick�s salary. Write an equation stating Alberto�s a
Alberto�s salary was $2000 greater than 4 times Nick�s salary. Write an equation stating Alberto�s and Nick�s salaries in terms of x and y. If Alberto's salary is x and Nick's is y, we have: [B]x = 4y + 2000 [/B](since greater than means we add)
Alexandra was given a gift card for a coffee shop. Each morning, Alexandra uses the card to buy one
Alexandra was given a gift card for a coffee shop. Each morning, Alexandra uses the card to buy one cup of coffee. The original amount of money on the gift card was $45 and each cup of coffee costs $2.50. Write an equation for A(x),A(x), representing the amount money remaining on the card after buying xx cups of coffee. We start with 45, and each cup of coffee decreases our balance by 2.50, so we subtract: [B]A(x) = 45 - 2.50x[/B]
Alexis is working at her schools bake sale. Each mini cherry pie sells for $4 and each mini peach pi
Alexis is working at her schools bake sale. Each mini cherry pie sells for $4 and each mini peach pie sells for $3. Alexis sells 25 pies and collects $84. How many pies of each kind does she sell? Let each cherry pie be c and each peach pie be p. We have the following equations: [LIST=1] [*]c + p = 25 [*]4c + 3p = 84 [/LIST] You can solve this system of equations 3 ways. [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c%2Bp%3D25&term2=4c+%2B+3p+%3D+84&pl=Substitution']Substitution Rule[/URL] [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c%2Bp%3D25&term2=4c+%2B+3p+%3D+84&pl=Elimination']Elimination Rule[/URL] [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c%2Bp%3D25&term2=4c+%2B+3p+%3D+84&pl=Cramers+Method']Cramers Rule[/URL] No matter which way you choose, you get [B]c = 9 and p = 16[/B].
Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the siste
Alice is 3 years younger than Barbara, and Barbara is 5 years younger than Carol. Together the sisters are 68 years old. How old is Barbara? Let a be Alice's age, b be Barbara's age, and c be Carol's age. We have 3 given equations: [LIST=1] [*]a = b - 3 [*]b = c - 5 [*]a + b + c = 68 [/LIST] Rearrange (2) c = b + 5 Now plug in (1) and (2) revised into (3). We want to isolate for b. a + b + c = 68 (b - 3) + b + (b + 5) = 68 Combine like terms: (b + b + b) + (5 - 3) = 68 3b + 2 = 68 Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2B2%3D68&pl=Solve']equation calculator[/URL], and we get b = [B]22[/B]
Alicia deposited $41 into her checking account. She wrote checks for $31 and $13. Now her account ha
Alicia deposited $41 into her checking account. She wrote checks for $31 and $13. Now her account has a balance of $81. How much did she have in her account to start with? We start with a balance of b. Depositing 41 means we add to the account balance: b + 41 Writing checks for 31 and 13 means we subtract from the account balance: b + 41 - 31 - 13 The final balance is 81, so we set b + 41 - 31 - 13 equal to 81: b + 41 - 31 - 13 = 81 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B41-31-13%3D81&pl=Solve']type this equation into our math engine[/URL] and we get: b = [B]84[/B]
Aliyah had $24 to spend on seven pencils. After buying them she had $1. How much did each pencil cos
Aliyah had $24 to spend on seven pencils. After buying them she had $1. How much did each pencil cost? Let each pencil cost p. We're given the following equation: 7p + 1 = 24 [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B1%3D24&pl=Solve']Type this equation into our search engine[/URL] and we get: p = [B]$3.29[/B]
Aliyah has $24 to spend on 7 pencils. After buying them she had $10. How much did each pencil cost?
Aliyah has $24 to spend on 7 pencils. After buying them she had $10. How much did each pencil cost? Let the cost of each pencil be p. The phrase [I]leftover[/I] means we add to the cost of the pencils after buying them. We're given the equation: 7p + 10 = 24 To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=7p%2B10%3D24&pl=Solve']type this equation into our search engine[/URL] and we get: p = [B]2[/B]
Allan built an additional room onto his house. The length of the room is 3 times the width. The peri
Allan built an additional room onto his house. The length of the room is 3 times the width. The perimeter of the room is 60 feet. What is the length of the room A room is a rectangle. We know the perimeter of a rectangle is: P = 2l + 2w We're given two equations: [LIST=1] [*]l = 3w [*]P = 60 [/LIST] Plug (1) and (2) into our rectangle perimeter formula: 2(3w) + w = 60 6w + w = 60 [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2Bw%3D60&pl=Solve']Type this equation into our search engine[/URL] to solve for w: w = 8.5714 Now plug w = 8.5714 into equation 1 to solve for l: l = 3(8.5714) l = [B]25.7142[/B]
Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the en
Alorah joins a fitness center. She pays for a year plus a joining fee of $35. If the cost for the entire year is $299, how much will she pay each month? We set up the cost function C(m) where m is the number of months of membership: C(m) = cost per month * m + joining fee Plugging in our numbers from the problem with 12 months in a year, we get: 12c + 35 = 299 To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=12c%2B35%3D299&pl=Solve']type it in our search engine [/URL]and we get: c = [B]22[/B]
Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age?
Alvin is 12 years younger than Elga. The sum of their ages is 60 . What is Elgas age? Let a be Alvin's age and e be Elga's age. We have the following equations: [LIST=1] [*]a = e - 12 [*]a + e = 60 [/LIST] Plugging in (1) to (2), we get: (e - 12) + e = 60 Grouping like terms: 2e - 12 = 60 Add 12 to each side: 2e = 72 Divide each side by 2 [B]e = 36[/B]
Alvin is 34 years younger than Elga. Elga is 3 times older than Alvin. What is Elgas age?
Alvin is 34 years younger than Elga. Elga is 3 times older than Alvin. What is Elgas age? Let a be Alvin's age. Let e be Elga's age. We're given: [LIST=1] [*]a = e - 34 [*]e = 3a [/LIST] Substitute (2) into (1): a = 3a - 34 [URL='https://www.mathcelebrity.com/1unk.php?num=a%3D3a-34&pl=Solve']Typing this equation into the search engine[/URL], we get a = 17 Subtitute this into Equation (2): e = 3(17) e = [B]51[/B]
Alyssa had 87 dollars to spend on 6 books. After buying them she had 15 dollars . How much did each
Alyssa had 87 dollars to spend on 6 books. After buying them she had 15 dollars . How much did each book cost ? Let b be the cost of each book. We're given: 87 - 6b = 15 [URL='https://www.mathcelebrity.com/1unk.php?num=87-6b%3D15&pl=Solve']Typing this equation into search engine[/URL], we get: [B]b = 12[/B]
Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for ea
Amara currently sells televisions for company A at a salary of $17,000 plus a $100 commission for each television she sells. Company B offers her a position with a salary of $29,000 plus a $20 commission for each television she sells. How many televisions would Amara need to sell for the options to be equal? Let the number of tv's be t. Set up the salary function S(t): S(t) = Commision * tv's sold + Salary Company A: S(t) = 100t + 17,000 Company B: S(t) = 20t + 29,000 The problem asks for how many tv's it takes to make both company salaries equal. So we set the S(t) functions equal to each other: 100t + 17000 = 20t + 29000 [URL='https://www.mathcelebrity.com/1unk.php?num=100t%2B17000%3D20t%2B29000&pl=Solve']Type this equation into our search engine[/URL] and we get: t = [B]150[/B]
Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and in
Amy and ryan operate a car dealing and repair service. For a car detailing (full wash outside and inside. Amy charges 40$ and Ryan charges 50$ . In addition they charge a hourly rate. Amy charges $35/h and ryan charges $30/h. How many hours does amy and ryan have to work to make the same amount of money? Set up the cost functions C(h) where h is the number of hours. [U]Amy:[/U] C(h) = 35h + 40 [U]Ryan:[/U] C(h) = 30h + 50 To make the same amount of money, we set both C(h) functions equal to each other: 35h + 40 = 30h + 50 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=35h%2B40%3D30h%2B50&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]2[/B]
An Amazon delivery package receives a bonus if he delivers a package to a costumer in 20 minutes plu
An Amazon delivery package receives a bonus if he delivers a package to a costumer in 20 minutes plus or minus 5 minutes. Which inequality or equation represents the drivers allotted time (x) to receive a bonus 20 plus 5 minutes = 25 minutes 20 minus 5 minutes = 15 minutes So we have the inequality: [B]15 <= x <= 25[/B]
An ancient Greek was said to have lived 1/4 of his live as a boy, 1/5 as a youth, 1/3 as a man, and
An ancient Greek was said to have lived 1/4 of his live as a boy, 1/5 as a youth, 1/3 as a man, and spent the last 13 years as an old man. How old was he when he died? Set up his life equation per time lived as a boy, youth, man, and old man 1/4 + 1/5 + 1/3 + x = 1. Using our [URL='http://www.mathcelebrity.com/gcflcm.php?num1=4&num2=3&num3=5&pl=LCM']LCM Calculator[/URL], we see the LCM of 3,4,5 is 60. This is our common denominator. So we have 15/60 + 12/60 + 20/60 + x/60 = 60/60 [U]Combine like terms[/U] x + 47/60 = 60/60 [U]Subtract 47/60 from each side:[/U] x/60 = 13/60 x = 13 out of the 60 possible years, so he was [B]60 when he died[/B].
An angle is 30 degrees less than 5 times it's complement. Find the angle.
An angle is 30 degrees less than 5 times it's complement. Find the angle. Let the angle be a. The complement of a is 90 - a. We're given the following equation: a = 5(90 - a) - 30 <-- Less means we subtract Multiplying though, we get: a = 450 - 5a - 30 a = 420 - 5a [URL='https://www.mathcelebrity.com/1unk.php?num=a%3D420-5a&pl=Solve']Typing this equation into our search engine[/URL], we get: a =[B] 70[/B]
An auto repair bill was $563. This includes $188 for parts and $75 for each hour of labor. Find the
An auto repair bill was $563. This includes $188 for parts and $75 for each hour of labor. Find the number of hours of labor Let the number of hours of labor be h. We have the cost function C(h): C(h) = Hourly Labor Rate * h + parts Given 188 for parts, 75 for hourly labor rate, and 563 for C(h), we have: 75h + 188 = 563 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=75h%2B188%3D563&pl=Solve']type it in our search engine[/URL] and we get: h = [B]5[/B]
An equilateral triangle has three sides of equal length. What is the equation for the perimeter of a
An equilateral triangle has three sides of equal length. What is the equation for the perimeter of an equilateral triangle if P = perimeter and S = length of a side? P = s + s + s [B]P = 3s[/B]
An executive invests $23,000, some at 8% and some at 4% annual interest. If he receives an annual re
An executive invests $23,000, some at 8% and some at 4% annual interest. If he receives an annual return of $1,560, how much is invested at each rate? Let x be the amount invested at 8% and y be the amount invested at 4%. We have two equations: [LIST=1] [*]x + y = 23,000 [*]0.08x + 0.04y = 1,560 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y+%3D+23000&term2=0.08x+%2B+0.04y+%3D+1560&pl=Cramers+Method']system of equations calculator[/URL], we get: [B]x = 16,000 y = 7,000[/B]
An experienced accountant can balance the books twice as fast as a new accountant. Working together
An experienced accountant can balance the books twice as fast as a new accountant. Working together it takes the accountants 10 hours. How long would it take the experienced accountant working alone? Person A: x/2 job per hour Person B: 1/x job per hour Set up our equation: 1/x + 1/(2x) = 1/10 Multiply the first fraction by 2/2 to get common denominators; 2/(2x) + 1/(2x) = 1/10 Combine like terms 3/2x = 1/10 Cross multiply: 30 = 2x Divide each side by 2: [B]x = 15[/B]
An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three tim
An irregular pentagon is a five sided figure. The two longest sides of a pentagon are each three times as long as the shortest side. The remaining two sides are each 8m longer than the shortest side. The perimeter of the Pentagon is 79m. Find the length of each side of the Pentagon. Let long sides be l. Let short sides be s. Let medium sides be m. We have 3 equations: [LIST=1] [*]2l + 2m + s = 79 [*]m = s + 8 [*]l = 3s [/LIST] Substitute (2) and (3) into (1): 2(3s) + 2(s + 8) + s = 79 Multiply through and simplify: 6s + 2s + 16 + s = 79 9s + 16 = 79 [URL='https://www.mathcelebrity.com/1unk.php?num=9s%2B16%3D79&pl=Solve']Using our equation calculator[/URL], we get [B]s = 7[/B]. This means from Equation (2): m = 7 + 8 [B]m = 15 [/B] And from equation (3): l = 3(7) [B]l = 21[/B]
An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the mea
An isosceles triangles non-congruent angle is 16 more than twice the congruent ones. What is the measure of all 3 angles? Let the congruent angles measurement be c. And the non-congruent angle measurement be n. We're given: [LIST=1] [*]n = 2c + 16 <-- Twice means we multiply by 2, and more than means we add 16 [*]2c + n = 180 <-- Since the sum of angles in an isosceles triangle is 180 [/LIST] Substitute (1) into (2): 2c + (2c + 16) = 180 Group like terms: 4c + 16 = 180 [URL='https://www.mathcelebrity.com/1unk.php?num=4c%2B16%3D180&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]c = 41[/B] Substituting this value into Equation 1, we get n = 2(41) + 16 n = 82 + 16 [B]n = 98[/B]
An oil tank contains 220.2 gallons of oil......
Start with 220.2 gallons of oil. Add 145.3 [U]more[/U] gallons 220.2 + 145.3 = 365.3 Now, figure out how much be pumped out to get down to 90. Call it x 365.3 - x = 90 Rearranging our equation, we have: x = 365.3 - 90 [B]x = 275.3[/B]
An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How ma
An orchard has 378 orange trees. The number of rows exceeds the number of trees per row by 3. How many trees are there in each row? We have r rows and t trees per row. We're give two equations: [LIST=1] [*]rt = 378 [*]r = t + 3 [/LIST] Substitute equation (2) into equation (1) for r: (t + 3)t = 378 Multiply through: t^2 + 3t = 378 We have a quadratic equation. To solve this equation, we [URL='https://www.mathcelebrity.com/quadratic.php?num=t%5E2%2B3t%3D378&pl=Solve+Quadratic+Equation&hintnum=+0']type it in our search engine [/URL]and we get: t = 18 and t = -21 Since t cannot be negative, we get trees per row (t): [B]t = 18[/B]
An orchard has 816 apple trees. The number of rows exceeds the number of trees per row by 10. How ma
An orchard has 816 apple trees. The number of rows exceeds the number of trees per row by 10. How many trees are there in each row? Let the rows be r and the trees per row be t. We're given two equations: [LIST=1] [*]rt = 816 [*]r = t + 10 [/LIST] Substitute equation (2) into equation (1) for r: (t + 10)t = 816 t^2 + 10t = 816 Subtract 816 from each side of the equation: t^2 + 10t - 816 = 816 - 816 t^2 + 10t - 816 = 0 We have a quadratic equation. To solve this, we [URL='https://www.mathcelebrity.com/quadratic.php?num=t%5E2%2B10t-816%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type it in our search engine [/URL]and we get: t = (24, -34) Since the number of trees per row can't be negative, we choose [B]24[/B] as our answer
Andrea has one hour to spend training for an upcoming race she completes her training by running ful
Andrea has one hour to spend training for an upcoming race she completes her training by running full speed in the distance of the race and walking back the same distance to cool down if she runs at a speed of 9 mph and walks back at a speed of 3 mph how long should she plan on spending to walk back Let r = running time. Let w = walking time We're given two equations [LIST=1] [*]r + w = 1 [*]9r = 3w [/LIST] Rearrange equation (1) by subtract r from each side: [LIST=1] [*]w = 1 - r [*]9r = 3w [/LIST] Now substitute equation (1) into equation (2): 9r = 3(1 - r) 9r = 3 - 3r To solve for r, [URL='https://www.mathcelebrity.com/1unk.php?num=9r%3D3-3r&pl=Solve']we type this equation into our search engine[/URL] and we get: r = 0.25 Plug this into modified equation (1) to solve for w, and we get: w = 1. 0.25 [B]w = 0.75[/B]
Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What
Angad was thinking of a number. Angad adds 20 to it, then doubles it and gets an answer of 53. What was the original number? The phrase [I]a number[/I] means an arbitrary variable, let's call it n. [LIST] [*]Start with n [*]Add 20 to it: n + 20 [*]Double it means we multiply the expression by 2: 2(n + 20) [*]Get an answer of 53: means an equation, so we set 2(n + 20) equal to 53 [/LIST] 2(n + 20) = 53 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=2%28n%2B20%29%3D53&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]6.5[/B]
Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 46 ho
Angelo is paid double time for each hour he works over 40 hours in a week. Last week he worked 46 hours and earned $624. What is his normal hourly rate? Let h be Angelo's hourly rate. We have: 40h + (46 - 40) * 2 * h = 624 40h + 6 * 2 * h = 624 40h + 12h = 624 Combine like terms: 52h = 624 [URL='https://www.mathcelebrity.com/1unk.php?num=52h%3D624&pl=Solve']Typing this equation into our search engine[/URL], we get [B]h = 12[/B].
Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Ke
Angie and Kenny play online video games. Angie buy 2 software packages and 4 months of game play. Kenny buys 1 software package and 1 month of game play. Each software package costs $25. If their total cost is $155, what is the cost of one month of game play. Let s be the cost of software packages and m be the months of game play. We have: [LIST] [*]Angie: 2s + 4m [*]Kenny: s + m [/LIST] We are given each software package costs $25. So the revised equations above become: [LIST] [*]Angie: 2(25) + 4m = 50 + 4m [*]Kenny: 25 + m [/LIST] Finally, we are told their combined cost is 155. So we add Angie and Kenny's costs together: 4m + 50 + 25 + m = 155 Combine like terms: 5m + 75 = 155 [URL='http://www.mathcelebrity.com/1unk.php?num=5m%2B75%3D155&pl=Solve']Typing this into our search engine[/URL], we get [B]m = 16[/B]
Angie is 11, which is 3 years younger than 4 times her sister's age.
Angie is 11, which is 3 years younger than 4 times her sister's age. Let her sister's age be a. We're given the following equation: 4a - 3 = 11 To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=4a-3%3D11&pl=Solve']type this equation into our math engine[/URL] and we get: [B]a = 3.5[/B]
Angular Momentum
Solves for any of the 4 variables in the angular momentum equation, L, V, M, and R
Anna has 50 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exa
Anna has 50 coins in her piggy bank. She notices that she only has dimes and pennies. If she has exactly four times as many pennies as dimes, how many pennies are in her piggy bank? Let d be the number of dimes, and p be the number of pennies. We're given: [LIST=1] [*]d + p = 50 [*]p = 4d [/LIST] Substitute (2) into (1) d + 4d = 50 [URL='https://www.mathcelebrity.com/1unk.php?num=d%2B4d%3D50&pl=Solve']Type that equation into our search engine[/URL]. We get: d = 10 Now substitute this into Equation (2): p = 4(10) [B]p = 40[/B]
Annulus
Calculates the area of an annulus and the equation of the annulus using the radius of the large and small concentric circles.
Antonio has a change jar that contains $3.65 in half dollars and nickels. He has 7 more nickels than
Antonio has a change jar that contains $3.65 in half dollars and nickels. He has 7 more nickels than half dollars. How many of each type of coin does he have? Let h be half dollars Let n be nickels We're given two equations: [LIST=1] [*]n = h + 7 [*]0.5h + 0.05n = 3.65 [/LIST] Substitute equation (1) into equation (2) for n: 0.5h + 0.05(h + 7) = 3.65 To solve this equation for h, we[URL='https://www.mathcelebrity.com/1unk.php?num=0.5h%2B0.05%28h%2B7%29%3D3.65&pl=Solve'] type it in our search engine[/URL] and we get: h = [B]6 [/B] To get n, we substitute h = 6 into equation (1) above: n = 6 + 7 n = [B]13[/B]
April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that
April, May and June have 90 sweets between them. May has three-quarters of the number of sweets that June has. April has two-thirds of the number of sweets that May has. How many sweets does June have? Let the April sweets be a. Let the May sweets be m. Let the June sweets be j. We're given the following equations: [LIST=1] [*]m = 3j/4 [*]a = 2m/3 [*]a + j + m = 90 [/LIST] Cross multiply #2; 3a = 2m Dividing each side by 2, we get; m = 3a/2 Since m = 3j/4 from equation #1, we have: 3j/4 = 3a/2 Cross multiply: 6j = 12a Divide each side by 12: a = j/2 So we have: [LIST=1] [*]m = 3j/4 [*]a = j/2 [*]a + j + m = 90 [/LIST] Now substitute equation 1 and 2 into equation 3: j/2 + j + 3j/4 = 90 Multiply each side by 4 to eliminate fractions: 2j + 4j + 3j = 360 To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%2B4j%2B3j%3D360&pl=Solve']type it in our search engine[/URL] and we get: j = [B]40[/B]
Arizona became a state in 1912. This was 5 years after Oklahoma became a state. Which equation can b
Arizona became a state in 1912. This was 5 years after Oklahoma became a state. Which equation can be used to find the year Oklahoma became a state? In what year did Oklahoma become a state? Let o be the year Oklahoma became a state: o = 1912 - 5 o = [B]1907[/B]
Arnie bought some bagels at 20 cents each. He ate 4, and sold the rest at 30 cents each. His profit
Arnie bought some bagels at 20 cents each. He ate 4, and sold the rest at 30 cents each. His profit was $2.40. How many bagels did he buy? Let x be the number of bagels Arnie sold. We have the following equation: 0.30(x - 4) - 0.20(4) = 2.40 Distribute and simplify: 0.30x - 1.20 - 0.8 = 2.40 Combine like terms: 0.30x - 2 = 2.40 Add 2 to each side: 0.30x = 4.40 Divide each side by 0.3 [B]x = 14.67 ~ 15[/B]
Arvin is twice as old as Cory. The sum of their ages is 42. What are their ages?
Arvin is twice as old as Cory. The sum of their ages is 42. What are their ages? Let Arvin's age be a. Let Cory's age be c. We're given two equations: [LIST=1] [*]a = 2c [*]a + c = 42 [/LIST] Plug equation (1) into equation (2): 2c + c = 42 [URL='https://www.mathcelebrity.com/1unk.php?num=2c%2Bc%3D42&pl=Solve']Plug this into our search engine[/URL] and we get: [B]c = 14[/B] Now, we plug c = 14 into equation 1 to solve for a: a = 2(14) [B]a = 28[/B]
Ashley age is 2 times Johns age. The sum of their ages is 63. What is Johns age?
Ashley age is 2 times Johns age. The sum of their ages is 63. What is Johns age? Let Ashley's age be a. Let John's age be j. We have two equations: [LIST=1] [*]a = 2j [*]a + j = 63 [/LIST] Now substitute (1) into (2) (2j) + j = 63 Combine like terms: 3j = 63 [URL='http://www.mathcelebrity.com/1unk.php?num=3j%3D63&pl=Solve']Typing 3j = 63 into our search engine[/URL], we get [B]j = 21[/B]
at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slic
at a bakery the cost of one cupcake and 2 slices of pie is $12.40. the cost of 2 cupcakes and 3 slices of pie costs $20.20. what is the cost of one cupcake? Let the number of cupcakes be c Let the number of pie slices be p Total Cost = Unit cost * quantity So we're given two equations: [LIST=1] [*]1c + 2p = 12.40 [*]2c + 3p = 20.20 [/LIST] We can solve this system of equations any one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=1c+%2B+2p+%3D+12.40&term2=2c+%2B+3p+%3D+20.20&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]c = 3.2[/B] [*]p = 4.6 [/LIST]
At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 m
At a carnival, the price of an adult ticket is $6 while a child ticket is $4. On a certain day, 30 more child tickets than adult tickets were sold. If a total of $6360 was collected from the total ticket sale that day, how many child tickets were sold? Let the number of adult tickets be a. Let the number of child tickets be c. We're given two equations: [LIST=1] [*]c = a + 30 [*]6a + 4c = 6360 [/LIST] Substitute equation (1) into equation (2): 6a + 4(a + 30) = 6360 Multiply through to remove parentheses: 6a + 4a + 120 = 6360 T[URL='https://www.mathcelebrity.com/1unk.php?num=6a%2B4a%2B120%3D6360&pl=Solve']ype this equation into our search engine[/URL] to solve for a and we get: a = 624 Now substitute a = 624 back into equation (1) to solve for c: c = 124 + 30 c = [B]154[/B]
At a concert there were 25 more women than men. The total number of people at the concert was 139. F
At a concert there were 25 more women than men. The total number of people at the concert was 139. Find the number of women and the number of men at the concert. Let men be m and women be w. We're given two equations. [LIST=1] [*]w = m + 25 [*]m + w = 139 [/LIST] Substitute equation (1) into equation (2): m + m + 25 = 139 To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%2B25%3D139&pl=Solve']type this equation into our search engine[/URL] and we get: m = [B]57 [/B] To find w, we substitute m = 57 into equation (1): w = 57 + 25 w = [B]82[/B]
At a festival, Cherly bought 5 ride tokens and 9 game tokens. She spent $59. Let x represent the cos
At a festival, Cherly bought 5 ride tokens and 9 game tokens. She spent $59. Let x represent the cost of ride tokens and let y represent the cost of game tokens. Write an equation in standard for that can be used to determine how much each type of token costs. We know that: Token Cost + Game Cost = Total Cost Since cost = price * quantity, we have: [B]5x + 9y = 59[/B]
At a football game, a vender sold a combined total of 117 sodas and hot dogs. The number of hot dogs
At a football game, a vender sold a combined total of 117 sodas and hot dogs. The number of hot dogs sold was 59 less than the number of sodas sold. Find the number of sodas sold and the number of hot dogs sold. [U]Let h = number of hot dogs and s = number of sodas. Set up our given equations:[/U] [LIST=1] [*]h + s = 117 [*]h = s - 59 [/LIST] [U]Substitute (2) into (1)[/U] (s - 59) + s = 117 [U]Combine s terms[/U] 2s - 59 = 117 [U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2s-59%3D117&pl=Solve']equation solver[/URL], we find:[/U] [B]s = 88 [/B] [U]Plug s = 88 into (2)[/U] h = 88 - 59 [B]h = 29[/B]
At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers fo
At a homecoming football game, the senior class sold slices of pizza for $.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers, and sales totaled $292.5. How many slices of pizza did they sell Let the number of pizza slices be p and the number of hamburgers be h. We're given two equations: [LIST=1] [*]p = h + 40 [*]1.35h + 0.75p = 292.50 [/LIST] [I]Substitute[/I] equation (1) into equation (2) for p: 1.35h + 0.75(h + 40) = 292.50 1.35h + 0.75h + 30 = 292.50 2.10h + 30 = 292.50 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.10h%2B30%3D292.50&pl=Solve']plug this equation into our search engine[/URL] and we get: h = 125 The problem asks for number of pizza slices sold (p). So we substitute our value above of h = 125 into equation (1): p = 125 + 40 p = [B]165[/B]
At a local fitness center, members pay an $8 membership fee and $3 for each aerobics class. Nonmembe
At a local fitness center, members pay an $8 membership fee and $3 for each aerobics class. Nonmembers pay $5 for each aerobics class. For what number of aerobics classes will the cost for members be equal to nonmembers? Set up two cost equations C(x): [LIST=1] [*]Members: C(x) = 8 + 3x [*]Nonmembers: C(x) = 5x [/LIST] Set the two cost equations equal to each other: 8 + 3x = 5x Subtract 3x from each side 2x = 8 Divide each side by 2 [B]x = 4[/B]
At the end of the 2021 NBA season, the NY Knicks had 10 more wins than losses. This NBA season the N
At the end of the 2021 NBA season, the NY Knicks had 10 more wins than losses. This NBA season the NY Knicks played a total of 72 times. Find a solution to this problem and explain. Let w be the number of wins Let l be the number of losses We're given two equations: [LIST=1] [*]w = l + 10 [*]l + w = 72 [/LIST] To solve this system of equations, substitute equation (1) into equation (2) for w: l + l + 10 = 72 To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2Bl%2B10%3D72&pl=Solve']type it in our math engine[/URL] and we get: l = [B]31 [/B] To solve for w, we substitute l = 31 into equation (1): w = 31 + 10 w = [B]41[/B]
At the end of the day, the temperature is -16�C. During the day it dropped 12�C. What was the temper
At the end of the day, the temperature is -16�C. During the day it dropped 12�C. What was the temperature in the morning? Write an equation to represent, then solve and verify your answer let the starting temperature be s. If the temperature dropped, that means we subtract, so we have the following equation: s - 12 = -16 To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=s-12%3D-16&pl=Solve']type it in our search engine[/URL] and we get: s = [B]-4[/B]
At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on
At the end of the week, Francesca had a third of her babysitting money left after spending $14.65 on a movie and popcorn and another $1.35 on a pen. How much did she earn babysitting? Let the original amount of money earned for babysitting be b. We're given: [LIST=1] [*]Start with b [*]Spending 14.65 for a movie means we subtract 14.65 from b: b - 14.65 [*]Spending 1.35 on a pen means we subtract another 1.35 from step 2: b - 14.65 - 1.35 [*]Francesca has a third of her money left. So we set step 3 equal to 1/3 of b [/LIST] b - 14.65 - 1.35 = b/3 Multiply each side of the equation by 3 to remove the fraction 3(b - 14.65 - 1.35) = 3b/3 3b - 43.95 - 4.05 = b To solve this equation for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b-43.95-4.05%3Db&pl=Solve']we type it in our search engine[/URL] and we get: b =[B] 24[/B]
Austin needs $240 to buy a new bike if he can save $16 per week and how many weeks can you purchase
Austin needs $240 to buy a new bike if he can save $16 per week and how many weeks can you purchase the bike? Set up the equation, where w equals the number of weeks needed. We have: 16w = 240 [URL='https://www.mathcelebrity.com/1unk.php?num=16w%3D240&pl=Solve']Typing this into our search engine[/URL], we get [B]w = 15[/B].
Ava is 4 times as old as Peter. What equation can be used to find Peter�s age?
Ava is 4 times as old as Peter. What equation can be used to find Peter�s age? [U]Assumptions[/U] Let a be Ava's age Let p be Peter's age We're given: a = 4p To find Peter's age, we divide each side of the equation by 4 to get: a/4 = 4p/4 p = [B]a/4[/B]
average of 16 and x is three. find x
average of 16 and x is three. find x Average of 16 and x is written as: (16 + x)/2 We set this equal to 3: (16 + x)/2 = 3 Cross multiply; x + 16 = 6 [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B16%3D6&pl=Solve']Type this equation into our search engine[/URL] and we get: x = [B]-10[/B]
B out of 6 is 12
B out of 6 is 12 b out of 6: b/6 The phrase [I]is[/I] means an equation, so we set b/6 equal to 12: [B]b/6 = 12[/B]
b/3d - h = 343 for b
b/3d - h = 343 for b A literal equation means we solve for one variable in terms of another variable or variables Add h to each side to isolate the b term: b/3d - h + h = 343 + h Cancel the h's on the left side, we get: b/3d = 343 + h Cross multiply: b = [B]3d(343 + h)[/B]
Bacteria in a petra dish doubles every hour. If there were 34 bacteria when the experiment began, wr
Bacteria in a petra dish doubles every hour. If there were 34 bacteria when the experiment began, write an equation to model this. Let h be the number of hours since the experiment began. Our equation is: [B]B(h) = 34(2^h)[/B]
Balancing Equations
Given 4 numbers, this will use the four operations: addition, subtraction, multiplication, or division to balance the equations if possible.
Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will
Barney has $450 and spends $3 each week. Betty has $120 and saves $8 each week. How many weeks will it take for them to have the same amount of money? Let w be the number of weeks that go by for saving/spending. Set up Barney's balance equation, B(w). Spending means we [U]subtract[/U] B(w) = Initial Amount - spend per week * w weeks B(w) = 450 - 3w Set up Betty's balance equation, B(w). Saving means we [U]add[/U] B(w) = Initial Amount + savings per week * w weeks B(w) = 120 + 8w The same amount of money means both of their balance equations B(w) are equal. So we set Barney's balance equal to Betty's balance and solve for w: 450 - 3w = 120 + 8w Add 3w to each side to isolate w: 450 - 3w + 3w = 120 + 8w + 3w Cancelling the 3w on the left side, we get: 450 = 120 + 11w Rewrite to have constant on the right side: 11w + 120 = 450 Subtract 120 from each side: 11w + 120 - 120 = 450 - 120 Cancelling the 120's on the left side, we get: 11w = 330 To solve for w, we divide each side by 11 11w/11 = 330/11 Cancelling the 11's on the left side, we get: w = [B]30 [MEDIA=youtube]ifG_q-utgJI[/MEDIA][/B]
Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign
Bawi solves a problem that has an answer of x = -4. He first added 7 to both sides of the equal sign, then divided by 3. What was the original equation [LIST=1] [*]If we added 7 to both sides, that means we had a minus 7 (-7) to start with as a constant. Since subtraction undoes addition. [*]If we divided by 3, this means we multiplied x by 3 to begin with. Since division undoes multiplication [/LIST] So we have the start equation: 3x - 7 If the answer was x = -4, then we plug this in to get our number on the right side of the equation: 3(-4) - 7 -12 - 7 -19 This means our original equation was: [B]3x - 7 = -19[/B] And if we want to solve this to prove our answer, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-7%3D-19&pl=Solve']type the equation into our search engine [/URL]and we get: x = -4
Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each p
Belle bought 30 pencils for $1560. She made a profit of $180. How much profit did she make on each pencil The cost per pencil is: 1560/30 = 52 Build revenue function: Revenue = Number of Pencils * Sales Price (s) Revenue = 30s The profit equation is: Profit = Revenue - Cost Given profit is 180 and cost is 1560, we have: 30s - 1560 = 180 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=30s-1560%3D180&pl=Solve']type this equation into our search engine[/URL] and we get: s = 58 This is sales for total profit. The question asks profit per pencil. Profit per pencil = Revenue per pencil - Cost per pencil Profit per pencil = 58 - 52 Profit per pencil = [B]6[/B]
Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money
Ben has $4.50 in quarters(Q) and dimes(D). a)Write an equation expressing the total amount of money in terms of the number of quarters and dimes. b)Rearrange the equation to isolate for the number of dimes (D) a) The equation is: [B]0.1d + 0.25q = 4.5[/B] b) Isolate the equation for d. We subtract 0.25q from each side of the equation: 0.1d + 0.25q - 0.25q = 4.5 - 0.25q Cancel the 0.25q on the left side, and we get: 0.1d = 4.5 - 0.25q Divide each side of the equation by 0.1 to isolate d: 0.1d/0.1 = (4.5 - 0.25q)/0.1 d = [B]45 - 2.5q[/B]
Ben is 3 times as old as Daniel and is also 4 years older than Daniel.
Ben is 3 times as old as Daniel and is also 4 years older than Daniel. Let Ben's age be b, let Daniel's age by d. We're given: [LIST=1] [*]b = 3d [*]b = d + 4 [/LIST] Substitute (1) into (2) 3d = d + 4 [URL='https://www.mathcelebrity.com/1unk.php?num=3d%3Dd%2B4&pl=Solve']Type this equation into our search engine[/URL], and we get [B]d = 2[/B]. Substitute this into equation (1), and we get: b = 3(2) [B]b = 6 [/B] So Daniel is 2 years old and Ben is 6 years old.
Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan.
Ben is 4 times as old as Ishaan and is also 6 years older than Ishaan. Let b be Ben's age and i be Ishaan's age. We're given: [LIST=1] [*]b = 4i [*]b = i + 6 [/LIST] Set (1) and (2) equal to each other: 4i = i + 6 [URL='https://www.mathcelebrity.com/1unk.php?num=4i%3Di%2B6&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]i = 2[/B] Substitute this into equation (1): b = 4(2) [B]b = 8 [/B] [I]Therefore, Ishaan is 2 years old and Ben is 8 years old.[/I]
Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of
Benny bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 47 cards left. How many cards did Benny start with? Let b be the number of baseball trading cards Benny started with. We have the following events: [LIST=1] [*]Benny buys 8 new cards, so we add 8 to get b + 8 [*]The dog ate half of his cards the next day, so Benny has (b + 8)/2 [*]We're told he has 47 cards left, so we set (b + 8)/2 equal to 47 [/LIST] (b + 8)/2 = 47 [B][U]Cross multiply:[/U][/B] b + 8 = 47 * 2 b + 8 = 94 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B8%3D94&pl=Solve']Type this equation into the search engine[/URL], we get [B]b = 86[/B].
Benny had 119 dollars to spend on 9 books. After buying them he had 11 dollars. How much did each bo
Benny had 119 dollars to spend on 9 books. After buying them he had 11 dollars. How much did each book cost ? Let each book cost "b". We have: 9b + 11 = 119 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=9b%2B11%3D119&pl=Solve']equation calculator[/URL], we get [B]b = 12[/B].
Benny had 90 dollars to spend on 7 books. After buying them he had 13 dollars. How much did each boo
Benny had 90 dollars to spend on 7 books. After buying them he had 13 dollars. How much did each book cost? Let each book cost be b. We have: 7b + 13 = 90 [URL='https://www.mathcelebrity.com/1unk.php?num=7b%2B13%3D90&pl=Solve']Typing this equation into the search engine[/URL], and you get: [B]b = 11[/B]
Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is
Beth is 5 years younger than celeste. Next year, their ages will have a sum equal to 57. How old is each now? Let b = Beth's age Let c = Celeste's age We are given: [LIST=1] [*]b = c - 5 [*]b + 1 + c + 1 = 57 [/LIST] Substitute (1) into (2) (c - 5) + 1 + c + 1 = 57 Group like terms: 2c - 3 = 57 [URL='https://www.mathcelebrity.com/1unk.php?num=2c-3%3D57&pl=Solve']Type 2c - 3 = 57 into our search engine[/URL], we get [B]c = 30[/B] Substitute c = 30 into Equation (1), we get: b = 30 - 5 [B]b = 25 [/B] Therefore, Beth is 25 and Celeste is 30.
Big John weighs 300 pounds and is going on a diet where he'll lose 3 pounds per week. Write an equat
Big John weighs 300 pounds and is going on a diet where he'll lose 3 pounds per week. Write an equation in slope-intercept form to represent this situation. [LIST] [*]The slope intercept form is y = mx + b [*]y is John's weight [*]x is the number of weeks [*]A 3 pound per week weight loss means -3 as the coefficient m [*]b = 300, John's starting weight [/LIST] [B]y = -3x + 300[/B]
Blueberries are $4.99 a pound. Diego buys b pounds of blueberries and pays $14.95.
Blueberries are $4.99 a pound. Diego buys b pounds of blueberries and pays $14.95. Since price * quantity = cost, we have the equation: 4.99b = 14.95 To solve for b, [URL='https://www.mathcelebrity.com/1unk.php?num=4.99b%3D14.95&pl=Solve']we type this equation into our search engine[/URL] and we get: b = [B]$3.00[/B]
Bob bought 10 note books and 4 pens for 18$. Bill bought 6 notebooks and 4 pens for 12$. Find the pr
Bob bought 10 note books and 4 pens for 18$. Bill bought 6 notebooks and 4 pens for 12$. Find the price of one note book and one pen. Let the price of each notebook be n. Let the price of each pen be p. We're given two equations: [LIST=1] [*]10n + 4p = 18 [*]6n + 4p = 12 [/LIST] Since we have matching coefficients for p, we subtract equation 1 from equation 2: (10 - 6)n + (4 - 4)p = 18 - 12 Simplifying and cancelling, we get: 4n = 6 [URL='https://www.mathcelebrity.com/1unk.php?num=4n%3D6&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]n = 1.5[/B] Now, substitute this value for n into equation (2): 6(1.5) + 4p = 12 Multiply through: 9 + 4p = 12 [URL='https://www.mathcelebrity.com/1unk.php?num=9%2B4p%3D12&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]p = 0.75[/B]
Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 fe
Bob fenced in his backyard. The perimeter of the yard is 22 feet, and the length of his yard is 5 feet. Use the perimeter formula to find the width of the rectangular yard in inches: P = 2L + 2W. Plugging our numbers in for P = 22 and L = 5, we get: 22 = 2(5) + 2W 22 = 10 + 2w Rewritten, we have: 10 + 2w = 22 [URL='https://www.mathcelebrity.com/1unk.php?num=10%2B2w%3D22&pl=Solve']Plug this equation into the search engine[/URL], we get: [B]w = 6[/B]
Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages
Bob finished reading his book in x days. Each day, he read 4 pages. His book has 28 pages Our equation for this is found by multiplying pages per day times number of days; 4x = 28 To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D28&pl=Solve']we type the equation into our search engine[/URL] and we get: x = [B]7[/B]
Bob has half as many quarters as dimes. He has $3.60. How many of each coin does he have?
Bob has half as many quarters as dimes. He has $3.60. How many of each coin does he have? Let q be the number of quarters. Let d be the number of dimes. We're given: [LIST=1] [*]q = 0.5d [*]0.25q + 0.10d = 3.60 [/LIST] Substitute (1) into (2): 0.25(0.5d) + 0.10d = 3.60 0.125d + 0.1d = 3.6 Combine like terms: 0.225d = 3.6 [URL='https://www.mathcelebrity.com/1unk.php?num=0.225d%3D3.6&pl=Solve']Typing this equation into our search engine[/URL], we're given: [B]d = 16[/B] Substitute d = 16 into Equation (1): q = 0.5(16) [B]q = 8[/B]
Bob is twice as old as Henry. The sum of their ages is 42. How old is Henry?
Bob is twice as old as Henry. The sum of their ages is 42. How old is Henry? Let Bob's age be b. Let Henry's age be h. We're given two equations: [LIST=1] [*]b = 2h [*]b + h = 42 [/LIST] Substitute b = 2h in equation 1 into equation 2 for b: 2h + h = 42 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2h%2Bh%3D42&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]14[/B]
Brice has 1200 in the bank. He wants to save a total of 3000 by depositing 40 per week from his payc
Brice has 1200 in the bank. He wants to save a total of 3000 by depositing 40 per week from his paycheck. How many weeks will it take until he saves 3000? Remaining Savings = 3,000 - 1,200 = 1,800 40 per week * x weeks = 1,800 40x = 1800 Divide each side of the equation by 40 [B]x = 45 weeks[/B]
Bruno is 3x years old and his son is x years old now. Their combined age is 40 years. How old is Bru
Bruno is 3x years old and his son is x years old now. Their combined age is 40 years. How old is Bruno Combined age means we add, so we have: 3x + x = 40 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x%2Bx%3D40&pl=Solve']type it in our search engine[/URL] and we get: x = 10 This means Bruno is: 3(10) = [B]30[/B]
Bud makes $400 more per month than maxine If their total income is $3600 how much does bud earn per
Bud makes $400 more per month than maxine If their total income is $3600 how much does bud earn per month Let Bud's earnings be b. Let Maxine's earnings be m. We're given two equations: [LIST=1] [*]b = m + 400 [*]b + m = 3600 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for b m + 400 + m = 3600 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B400%2Bm%3D3600&pl=Solve']type it in our search engine[/URL] and we get: m = 1600 To solve for b, we substitute m = 1600 into equation (1) above: b = 1600 + 400 b = [B]2200[/B]
Budget Line Equation
Solves for any one of the 5 items in the standard budget line equation:
Income (I)
Quantity of x = Qx
Quantity of y = Qy
Price of x = Px
Price of y = Py
Building A is 150 feet shorter than Building B. The height of both building is 1530 feet. Find the h
Building A is 150 feet shorter than Building B. The height of both building is 1530 feet. Find the height of both building A and B. Let a be the height of building A Let b be the height of building B We're given two equations: [LIST=1] [*]a = b - 150 [*]a + b = 1530 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for a: (b - 150) + b = 1530 To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b-150%2Bb%3D1530&pl=Solve']type it in our search engine[/URL] and we get: b = [B]840[/B] To solve for a, we substitute b = 840 into equation (1): a = 840 - 150 a = [B]690[/B]
by + 2/3 = c for y
by + 2/3 = c for y Subtract 2/3 from each side of the literal equation: by + 2/3 - 2/3 = c - 2/3 Cancel the 2/3 on the left side to get: by = c - 2/3 Divide each side by b to isolate y: by/b = (c - 2/3)/b Cancel the b's on the left side to get: y = [B](c - 2/3)/b[/B]
b^2 - 6 = 5an for a
b^2 - 6 = 5an for a Divide each side of the equation by 5n to isolate a: (b^2 - 6)/5n = 5an/5n Cancel the 5n on the right side and we get: a = [B](b^2 - 6)/5n[/B]
Caleb earns points on his credit card that he can use towards future purchases.
Let f = dollars spent on flights, h dollars spent on hotels, and p dollars spent on all other purchases. [U]Set up our equations:[/U] (1) 4f + 2h + p = 14660 (2) f + h + p = 9480 (3) f = 2h + 140 [U]First, substitute (3) into (2)[/U] (2h + 140) + h + p = 9480 3h + p + 140 = 9480 3h + p = 9340 [U]Subtract 3h to isolate p to form equation (4)[/U] (4) p = 9340 - 3h [U]Take (3) and (4), and substitute into (1)[/U] 4(2h + 140) + 2h + (9340 - h) = 14660 [U]Multiply through[/U] 8h + 560 + 2h + 9340 - 3h = 14660 [U]Combine h terms and constants[/U] (8 + 2 - 3)h + (560 + 9340) = 14660 7h + 9900 = 14660 [U]Subtract 9900 from both sides:[/U] 7h = 4760 [U]Divide each side by 7[/U] [B]h = 680[/B] [U]Substitute h = 680 into equation (3)[/U] f = 2(680) + 140 f = 1360 + 140 [B]f = 1,500[/B] [U] Substitute h = 680 and f = 1500 into equation (2)[/U] 1500 + 680 + p = 9480 p + 2180 = 9480 [U]Subtract 2180 from each side:[/U] [B]p = 7,300[/B]
Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appr
Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations. Let Cam's age be c. Let Lara's age be l. We're given two equations: [LIST=1] [*]c = l + 3 <-- older means we add [*]c + l = 63 <-- combined ages mean we add [/LIST] Substitute equation (1) into equation (2): l + 3 + l = 63 Combine like terms to simplify our equation: 2l + 3 = 63 To solve for l, [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B3%3D63&pl=Solve']we type this equation into our search engine[/URL] and we get: l = [B]30[/B] Now, we plug l = 30 into equation (1) to solve for c: c = 30 + 3 c = [B]33[/B]
Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appr
Cam is 3 years older than Lara. If their combined age is 63, determine their ages by solving an appropriate pair of equations. Let Cam's age be c. Let Lara's age be l. We're given two equations: [LIST=1] [*]c = l + 3 (Since older means we add) [*]c + l = 63 [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for c: l + 3 + l = 63 To solve this equation for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l%2B3%2Bl%3D63&pl=Solve']type it in our search engine [/URL]and we get: l = [B]30 [/B] Now, we take l = 30 and substitute it in equation (1) to solve for c: c = 30 + 3 c = [B]33[/B]
Carlos was asked to write an equivalent equation to 2x/5 = 1 - x. he wrote it as 2x = 1 - 5x. do you
Carlos was asked to write an equivalent equation to 2x/5 = 1 - x. he wrote it as 2x = 1 - 5x. do you agree with his conclusion? explain your answer for x Cross multiply 2x/5 = 1 - x 2x = 5(1 - x) 2x = 5 - 5x I disagree with his conclusion. He forgot to multiply the 5 through to [B]both terms[/B]
Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she
Carly has already written 35 of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months. Let m be the number of months. We have the pages written function P(m) as: P(m) = 12m + 35 The problem asks for P(5): P(5) = 12(5) + 35 P(5) = 60 + 35 P(5) = [B]95[/B]
Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month unti
Carly has already written 35 pages of a novel. She plans to write 12 additional pages per month until she is finished. Write and solve a linear equation to find the total number of pages written at 5 months. Set up the equation where m is the number of months: pages per month * m + pages written already 12m + 35 The problems asks for m = 5: 12(5) + 35 60 + 35 [B]95 pages[/B]
Cars and trucks are the most popular vehicles. last year, the number of cars sold was 39,000 more th
Cars and trucks are the most popular vehicles. last year, the number of cars sold was 39,000 more than 3 times the number of trucks sold. There were 216,000 cars sold last year. Write an equation that can be used to find the number of trucks, t, sold last year. Let c be the number of cars. Let t be the number of trucks. We're given two equations: [LIST=1] [*]c = 3t + 39000 [*]c + t = 216000 [/LIST] Substitute equation (1) into equation (2) for c: 3t + 39000 + t = 216000 To solve this equation for t, [URL='https://www.mathcelebrity.com/1unk.php?num=3t%2B39000%2Bt%3D216000&pl=Solve']we type it in our math engine [/URL]and we get: t = [B]44,250[/B]
Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her
Casey is 26 years old. Her daughter Chloe is 4 years old. In how many years will Casey be double her daughter's age Declare variables for each age: [LIST] [*]Let Casey's age be c [*]Let her daughter's age be d [*]Let n be the number of years from now where Casey will be double her daughter's age [/LIST] We're told that: 26 + n = 2(4 + n) 26 + n = 8 + 2n Solve for [I]n[/I] in the equation 26 + n = 8 + 2n [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables n and 2n. To do that, we subtract 2n from both sides n + 26 - 2n = 2n + 8 - 2n [SIZE=5][B]Step 2: Cancel 2n on the right side:[/B][/SIZE] -n + 26 = 8 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 26 and 8. To do that, we subtract 26 from both sides -n + 26 - 26 = 8 - 26 [SIZE=5][B]Step 4: Cancel 26 on the left side:[/B][/SIZE] -n = -18 [SIZE=5][B]Step 5: Divide each side of the equation by -1[/B][/SIZE] -1n/-1 = -18/-1 n = [B]18[/B] Check our work for n = 18: 26 + 18 ? 8 + 2(18) 44 ? 8 + 36 44 = 44
Cathy wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another
Cathy wants to buy a gym membership. One gym has a $150 joining fee and costs $35 per month. Another gym has no joining fee and costs $60 per month. a. In how many months will both gym memberships cost the same? What will that cost be? Set up cost equations where m is the number of months enrolled: [LIST=1] [*]C(m) = 35m + 150 [*]C(m) = 60m [/LIST] Set them equal to each other: 35m + 150 = 60m [URL='http://www.mathcelebrity.com/1unk.php?num=35m%2B150%3D60m&pl=Solve']Pasting the equation above into our search engine[/URL], we get [B]m = 6[/B].
center (3, -2), radius = 4
center (3, -2), radius = 4 To see the general form or standard form, you can check out this link: [URL='http://Circle Equations']https://www.mathcelebrity.com/eqcircle.php?h=3&k=-2&r=4&d1=1&d2=1&d3=2&d4=4&calc=1&ceq=&pl=Calculate[/URL]
Charlie buys a 40 pound bag of cat food. His cat eats a 1/2 pound of food per day.
Charlie buys a 40 pound bag of cat food. His cat eats a 1/2 pound of food per day. Set up an equation: 1/2x = 40 where x is the number of days Multiply through by 2 [B]x = 80[/B]
Chinese Remainder Theorem
Given a set of modulo equations in the form:
x ≡ a mod b
x ≡ c mod d
x ≡ e mod f
the calculator will use the Chinese Remainder Theorem to find the lowest possible solution for x in each modulus equation.
Given that the ni portions are not pairwise coprime and you entered two modulo equations, then the calculator will attempt to solve using the Method of Successive Subsitution
Cholesterol Equation
Solves for each of the 4 following cholesterol equation items:
1) Total Cholesterol
2) High Density Lipoproteins (HDL) Good Cholesterol
3) Low Density Lipoproteins (LDL) Bad Cholesterol
4) Triglycerides
Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to
Choose the equation of a line in standard form that satisfies the given conditions. perpendicular to 4x + y = 8 through (4, 3). Step 1: Find the slope of the line 4x + y = 8. In y = mx + b form, we have y = -4x + 8. The slope is -4. To be perpendicular to a line, the slope must be a negative reciprocal of the line it intersects with. Reciprocal of -4 = -1/4 Negative of this = -1(-1/4) = 1/4 Using our [URL='https://www.mathcelebrity.com/slope.php?xone=4&yone=3&slope=+0.25&xtwo=3&ytwo=2&bvalue=+&pl=You+entered+1+point+and+the+slope']slope calculator[/URL], we get [B]y = 1/4x + 2[/B]
Chord
Solves for any of the 3 items in the Chord of a Circle equation, Chord Length (c), Radius (r), and center to chord midpoint (t).
Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse i
Chris, Alex and Jesse are all siblings in the same family. Alex is 5 years older than chris. Jesse is 6 years older than Alex. The sum of their ages is 31 years. How old is each one of them? Set up the relational equations where a = Alex's age, c = Chris's aged and j = Jesse's age [LIST=1] [*]a = c + 5 [*]j = a + 6 [*]a + c + j = 31 [*]Rearrange (1) in terms of c: c = a - 5 [/LIST] [U]Plug in (4) and (2) into (3)[/U] a + (a - 5) + (a + 6) = 31 [U]Combine like terms:[/U] 3a + 1 = 31 [U]Subtract 1 from each side[/U] 3a = 30 [U]Divide each side by 3[/U] [B]a = 10[/B] [U]Plug in 1 = 10 into Equation (4)[/U] c = 10 - 5 [B]c = 5[/B] Now plug 1 = 10 into equation (2) j = 10 + 6 [B]j = 16[/B]
Circle Equation
This calculates the standard equation of a circle and general equation of a circle from the following given items:
* A center (h,k) and a radius r
* A diameter A(a1,a2) and B(b1,b2)
This also allows you to enter a standard or general form equation so that the center (h,k) and radius r can be determined.
Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends,
Clark wants to give some baseball cards to his friends. If he gives 6 cards to each of his friends, he will have 5 cards left. If he gives 8 cards to each of his friends, he will need 7 more cards. How many friends is the giving the cards to? Let the number of friends Clark gives his cards to be f. Let the total amount of cards he gives out be n. We're given 2 equations: [LIST=1] [*]6f + 5 = n [*]8f - 7 = n [/LIST] Since both equations equal n, we set these equations equal to each other 6f + 5 = 8f - 7 To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=6f%2B5%3D8f-7&pl=Solve']type this equation into our search engine[/URL] and we get: f = [B]6 [/B] To check our work, we plug in f = 6 into each equation: [LIST=1] [*]6(6) + 5 = 36 + 5 = 41 [*]8(6) - 7 = 48 - 7 = 41 [/LIST] So this checks out. Clark has 41 total cards which he gives to 6 friends.
Cole and Finn are roommates. They paid three months rent and a $200 security deposit when they signe
Cole and Finn are roommates. They paid three months rent and a $200 security deposit when they signed the lease. In total, they paid $1,850. What is the rent for one month? Write an equation and solve it. Equation, let m = rent for one month 3m + 200 = 1,850 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3m%2B200%3D1850&pl=Solve']Equation Solver[/URL], we get [B]m = 550[/B].
Colin was thinking of a number. Colin divides by 8, then adds 1 to get an answer of 2. What was the
Colin was thinking of a number. Colin divides by 8, then adds 1 to get an answer of 2. What was the original number? Let the number be n. Divide by 8: n/8 Then add 1: n/8 + 1 The phrase [I]get an answer[/I] of means an equation, so we set n/8 + 1 equal to 2: n/8 + 1 = 2 To solve for n, we subtract 1 from each side to isolate the n term: n/8 + 1 - 1 = 2 - 1 Cancel the 1's on the left side, we get: n/8 = 1 Cross multiply: n = 8*1 n = [B]8[/B]
Company a charges $25 plus $0.10 a mile. Company b charges $20 plus $0.15 per mile. How far would yo
Company a charges $25 plus $0.10 a mile. Company b charges $20 plus $0.15 per mile. How far would you need to travel to get each charge to be the same? Let x be the number of miles traveled Company A charge: C = 25 + 0.10x Company B charge: C = 20 + 0.15x Set up an equation find out when the charges are the same. 25 + 0.10x = 20 + 0.15x Combine terms and simplify 0.05x = 5 Divide each side of the equation by 0.05 to isolate x x = [B]100[/B]
Company A rents copy machines for $300 a month plus $0.05 per copy. Company B charges $600 plus $0.0
Company A rents copy machines for $300 a month plus $0.05 per copy. Company B charges $600 plus $0.01 per copy. For which number of copies do the two companies charge the same amount? With c as the number of copies, we have: Company A Cost = 300 + 0.05c Company B Cost = 600 + 0.01c Set them equal to each other 300 + 0.05c = 600 + 0.01c Use our [URL='http://www.mathcelebrity.com/1unk.php?num=300%2B0.05c%3D600%2B0.01c&pl=Solve']equation solver[/URL] to get: [B]c = 7,500[/B]
Connor runs 2 mi more each day than David. The sum of the distances they run each week is 56 mi. How
Connor runs 2 mi more each day than David. The sum of the distances they run each week is 56 mi. How far does David run each day? Let Connor's distance be c Let David's distance be d We're given two equations: [LIST=1] [*]c = d + 2 [*]7(c + d) = 56 [/LIST] Simplifying equation 2 by dividing each side by 7, we get: [LIST=1] [*]c = d + 2 [*]c + d = 8 [/LIST] Substitute equation (1) into equation (2) for c d + 2 + d = 8 To solve for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=d%2B2%2Bd%3D8&pl=Solve']type this equation into our calculation engine[/URL] and we get: d = [B]3[/B]
Consider the following 15 numbers 1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20 - The mean o
Consider the following 15 numbers 1, 2, y - 4, 4, 5, x, 6, 7, 8, y, 9, 10, 12, 3x, 20 - The mean of the last 10 numbers is TWICE the mean of the first 10 numbers - The sum of the last 2 numbers is FIVE times the sum of the first 3 numbers (i) Calculate the values of x and y We're given two equations: [LIST=1] [*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = 2(1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/10 [*]3x - 20 = 5(1 + 2 + y - 4) [/LIST] Let's evaluate and simplify: [LIST=1] [*](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10 = (1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5 [*]3x - 20 = 5(y - 1) [/LIST] Simplify some more: [URL='https://www.mathcelebrity.com/polynomial.php?num=x%2B6%2B7%2B8%2By%2B9%2B10%2B12%2B3x%2B20&pl=Evaluate'](x + 6 + 7 + 8 + y + 9 + 10 + 12 + 3x + 20)/10[/URL] = (4x + y + 72)/10 [URL='https://www.mathcelebrity.com/polynomial.php?num=1%2B2%2By-4%2B4%2B5%2Bx%2B6%2B7%2B8%2By&pl=Evaluate'](1 + 2 + y - 4 + 4 + 5 + x + 6 + 7 + 8 + y)/5[/URL] = (2y + x + 29)/5 5(y - 1) = 5y - 5 So we're left with: [LIST=1] [*](4x + y + 72)/10 = (2y + x + 29)/5 [*]3x - 20 = 5y - 5 [/LIST] Cross multiply equations in 1, we have: 5(4x + y + 72) = 10(2y + x + 29) 20x + 5y + 360 = 20y + 10x + 290 We have: [LIST=1] [*]20x + 5y + 360 = 20y + 10x + 290 [*]3x - 20 = 5y - 5 [/LIST] Combining like terms: [LIST=1] [*]10x - 15y = -70 [*]3x - 5y = 15 [/LIST] Now we have a system of equations which we can solve any of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10x+-+15y+%3D+-70&term2=3x+-+5y+%3D+15&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: (x, y) = [B](-115, -72)[/B]
Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve
Consider the formula for the area of a trapezoid: A=12h(a+b) . Is it mathematically simpler to solve for a, b, or h? Why? Solve for each of these variables to demonstrate. The variable "h" is the easiest to solve for. Because you only have one step. Let's review: Divide each side of the equation by 12(a + b) h = 12(a + b)/A Solving for "a", we two steps. Divide each side by 12h: A/12h = a + b Subtract b from each side a = A/12h - b Solving for "b" takes two steps as well. Divide each side by 12h: A/12h = a + b Subtract a from each side b = A/12h - a
Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total
Country A produces about 7 times the amount of diamonds in carats produce in Country B. If the total produced in both countries is 40,000,000 carats, find the amount produced in each country. Set up our two given equations: [LIST=1] [*]A = 7B [*]A + B = 40,000,000 [/LIST] Substitute (1) into (2) (7B) + B = 40,000,000 Combine like terms 8B = 40,000,000 Divide each side by 8 [B]B = 5,000,000[/B] Substitute this into (1) A = 7(5,000,000) [B]A = 35,000,000[/B]
Cubic Equation
Solves for cubic equations in the form ax3 + bx2 + cx + d = 0 using the following methods:
1) Solve the long way for all 3 roots and the discriminant Δ
2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.
d - f^3 = 4a for a
d - f^3 = 4a for a Solve this literal equation for a: Divide each side of the equation by 4: (d - f^3)/4 = 4a/4 Cancel the 4's on the right side, and rewrite with our variable to solve for on the left side: a = [B](d - f^3)/4[/B]
Dakota needs a total of $400 to buy a new bicycle. He has $40 saved. He earns $15 each week deliveri
Dakota needs a total of $400 to buy a new bicycle. He has $40 saved. He earns $15 each week delivering newspapers. How many weeks will Dakota have to deliver papers to have enough money to buy the bicycle? Let w be the number of weeks of delivering newspapers. We have the equation: 15w + 40 = 400 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=15w%2B40%3D400&pl=Solve']type this equation into our search engine[/URL] and we get: w = [B]24[/B]
Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of h
Dan bought 7 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 26 cards left. How many cards did Dan start with? Let the starting amount of cards be s. We're given: [LIST] [*]Dan bought 7 new cards: s + 7 [*]The dog ate half of his collection. This means he's left with half, or (s + 7)/2 [*]Now, he's got 26 cards left. So we set up the following equation: [/LIST] (s + 7)/2 = 26 Cross multiply: s + 7 = 26 * 2 s + 7 = 52 To solve for s, [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B7%3D52&pl=Solve']we plug this equation into our search engine[/URL] and we get: s = [B]45[/B]
Dan bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of h
Dan bought 8 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 30 cards left. How many cards did Dan start with? Let the original collection count of cards be b. So we have (b + 8)/2 = 30 Cross multiply: b + 8 = 30 * 2 b + 8 = 60 [URL='http://www.mathcelebrity.com/1unk.php?num=b%2B8%3D60&pl=Solve']Use the equation calculator[/URL] [B]b = 52 cards[/B]
Dan makes 9 dollars for each hour of work. Write an equation to represent his total pay p after work
Dan makes 9 dollars for each hour of work. Write an equation to represent his total pay p after working h hours. We know that pay (p) on an hourly basis (h) equals: p = Hourly Rate * h We're given an hourly rate of 9, so we have: p = [B]9h[/B]
Dan's school is planning a field trip to an art museum. Bus company A charges a $60 rental fee plus
Dan's school is planning a field trip to an art museum. Bus company A charges a $60 rental fee plus $4 per student. Bus company B charges $150 plus $2 per student. How many students would have to go for the cost to be the same? [U]Set up Company A's cost equation C(s) where s is the number of students[/U] C(s) = Cost per student * s + Rental Fee C(s) = 4s + 60 [U]Set up Company B's cost equation C(s) where s is the number of students[/U] C(s) = Cost per student * s + Rental Fee C(s) = 2s + 150 The problem asks for s where both C(s) equations would be equal. So we set Company A and Company B's C(s) equal to each other: 4s + 60 = 2s + 150 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B60%3D2s%2B150&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]45[/B]
Daniel is 41 inches tall. He is 3/5 as tall as his brother. How tall is his brother?
Daniel is 41 inches tall. He is 3/5 as tall as his brother. How tall is his brother? We set Daniel's brother's height at h. We have: 3h/5 = 41 To solve this equation for h, we [URL='https://www.mathcelebrity.com/prop.php?num1=3h&num2=41&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: [B]h = 68.3333 or 68 & 1/3[/B]
Daniel is 6cm taller than Kamala. If their total height is 368cm, how tall is Kamala?
Daniel is 6cm taller than Kamala. If their total height is 368cm, how tall is Kamala? Let Daniel's height be d. Let Kamala's height be k. We're given two equations: [LIST=1] [*]d = k + 6 [*]d + k = 368 [/LIST] Substitute equation (1) into equation (2) for d: k + 6 + k = 368 To solve for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=k%2B6%2Bk%3D368&pl=Solve']type this equation into our search engine[/URL] and we get: k = [B]181[/B]
David has b dollars in his bank account; Claire has three times as much money as David. The sum of t
David has b dollars in his bank account; Claire has three times as much money as David. The sum of their money is $240. How much money does Claire have? David has b Claire has 3b since three times as much means we multiply b by 3 The sum of their money is found by adding David's bank balance to Claire's bank balance to get the equation: 3b + b = 240 To solve for b, [URL='https://www.mathcelebrity.com/1unk.php?num=3b%2Bb%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get: b = 60 So David has 60 dollars in his bank account. Therefore, Claire has: 3(60) = [B]180[/B]
DeAndre is a spelunker (someone who explores caves). One day DeAndre is exploring a cave that has a
DeAndre is a spelunker (someone who explores caves). One day DeAndre is exploring a cave that has a series of ladders going down into the depths. Every ladder is exactly 10 feet tall, and there is no other way to descend or ascend (the other paths in the cave are flat). DeAndre starts at 186 feet in altitude, and reaches a maximum depth of 86 feet in altitude.Write an equation for DeAndre's altitude, using x to represent the number of ladders DeAndre used (hint: a ladder takes DeAndre down in altitude, so the coefficient should be negative). Set up a function A(x) for altitude, where x is the number of ladders used. Each ladder takes DeAndre down 10 feet, so this would be -10x. And DeAndre starts at 186 feet, so we'd have: [B]A(x) = 186 - 10x[/B]
Denise buys a soda for 90 cents, a candy bar for $1.20 and a bag of chips for $2.90. Assuming a 3.5
Denise buys a soda for 90 cents, a candy bar for $1.20 and a bag of chips for $2.90. Assuming a 3.5 percent sales tax, how much change would she receive from a $10 bill 1. Change = $10 - Total Bill Total Bill = (Soda + Candy Bar + Bag of Chips) * 1.035 Total Bill = ($0.90 + $1.20 + $2.90) * 1.035 Total Bill = $5 * 1.035 2. Total Bill = $5.18 Plug Equation (2) into Equation (1), we have: Change = $10 - $5.18 Change = [B]$4.82[/B]
Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up
Deon opened his account starting with $650 and he is going to take out $40 per month. Mai opened up her account with a starting amount of $850 and is going to take out $65 per month. When would the two accounts have the same amount of money? We set up a balance equation B(m) where m is the number of months. [U]Set up Deon's Balance equation:[/U] Withdrawals mean we subtract from our current balance B(m) = Starting Balance - Withdrawal Amount * m B(m) = 650 - 40m [U]Set up Mai's Balance equation:[/U] Withdrawals mean we subtract from our current balance B(m) = Starting Balance - Withdrawal Amount * m B(m) = 850 - 65m When the two accounts have the same amount of money, we can set both balance equations equal to each other and solve for m: 650 - 40m = 850 - 65m Solve for [I]m[/I] in the equation 650 - 40m = 850 - 65m [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables -40m and -65m. To do that, we add 65m to both sides -40m + 650 + 65m = -65m + 850 + 65m [SIZE=5][B]Step 2: Cancel -65m on the right side:[/B][/SIZE] 25m + 650 = 850 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 650 and 850. To do that, we subtract 650 from both sides 25m + 650 - 650 = 850 - 650 [SIZE=5][B]Step 4: Cancel 650 on the left side:[/B][/SIZE] 25m = 200 [SIZE=5][B]Step 5: Divide each side of the equation by 25[/B][/SIZE] 25m/25 = 200/25 m = [B]8[/B]
devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage
devaughn,sageis2timessydneysage,thesumoftheiragesis78,whatissydneysage Let d be Devaughn's age. Let s be Sydney's age. We have two equations: [LIST=1] [*]d = 2s [*]d + s = 78 [/LIST] Substitute (1) into (2) 2s + s = 78 3s = 78 Entering [URL='http://www.mathcelebrity.com/1unk.php?num=3s%3D78&pl=Solve']3x = 78 into the search engine[/URL], we get [B]s = 26[/B].
Diana earns $8.50 working as a lifeguard. Write an equation to find Dianas money earned m for any nu
Diana earns $8.50 working as a lifeguard. Write an equation to find Dianas money earned m for any numbers of hours h Set up the revenue function: [B]R = 8.5h[/B]
difference between 2 positive numbers is 3 and the sum of their squares is 117
difference between 2 positive numbers is 3 and the sum of their squares is 117 Declare variables for each of the two numbers: [LIST] [*]Let the first variable be x [*]Let the second variable be y [/LIST] We're given 2 equations: [LIST=1] [*]x - y = 3 [*]x^2 + y^2 = 117 [/LIST] Rewrite equation (1) in terms of x by adding y to each side: [LIST=1] [*]x = y + 3 [*]x^2 + y^2 = 117 [/LIST] Substitute equation (1) into equation (2) for x: (y + 3)^2 + y^2 = 117 Evaluate and simplify: y^2 + 3y + 3y + 9 + y^2 = 117 Combine like terms: 2y^2 + 6y + 9 = 117 Subtract 117 from each side: 2y^2 + 6y + 9 - 117 = 117 - 117 2y^2 + 6y - 108 = 0 This is a quadratic equation: Solve the quadratic equation 2y2+6y-108 = 0 With the standard form of ax2 + bx + c, we have our a, b, and c values: a = 2, b = 6, c = -108 Solve the quadratic equation 2y^2 + 6y - 108 = 0 The quadratic formula is denoted below: y = -b � sqrt(b^2 - 4ac)/2a [U]Step 1 - calculate negative b:[/U] -b = -(6) -b = -6 [U]Step 2 - calculate the discriminant ?:[/U] ? = b2 - 4ac: ? = 62 - 4 x 2 x -108 ? = 36 - -864 ? = 900 <--- Discriminant Since ? is greater than zero, we can expect two real and unequal roots. [U]Step 3 - take the square root of the discriminant ?:[/U] ?? = ?(900) ?? = 30 [U]Step 4 - find numerator 1 which is -b + the square root of the Discriminant:[/U] Numerator 1 = -b + ?? Numerator 1 = -6 + 30 Numerator 1 = 24 [U]Step 5 - find numerator 2 which is -b - the square root of the Discriminant:[/U] Numerator 2 = -b - ?? Numerator 2 = -6 - 30 Numerator 2 = -36 [U]Step 6 - calculate your denominator which is 2a:[/U] Denominator = 2 * a Denominator = 2 * 2 Denominator = 4 [U]Step 7 - you have everything you need to solve. Find solutions:[/U] Solution 1 = Numerator 1/Denominator Solution 1 = 24/4 Solution 1 = 6 Solution 2 = Numerator 2/Denominator Solution 2 = -36/4 Solution 2 = -9 [U]As a solution set, our answers would be:[/U] (Solution 1, Solution 2) = (6, -9) Since one of the solutions is not positive and the problem asks for 2 positive number, this problem has no solution
Difference between 23 and y is 12
Difference between 23 and y 23 - y Is, means equal to, so we set 23 - y equal to 12 [B]23 - y = 12 [/B] If you need to solve this algebraic expression, use our [URL='http://www.mathcelebrity.com/1unk.php?num=23-y%3D12&pl=Solve']equation calculator[/URL]: [B]y = 11[/B]
Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages.
Dina is twice as old as Andrea. The sum of their age is 72. Find their present ages. Let d be Dina's age. Let a be Andrea's age. We're given: [LIST=1] [*]d = 2a <-- Twice means multiply by 2 [*]a + d = 72 [/LIST] Substitute equation (1) into equation (2): a + 2a = 72 [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B2a%3D72&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]a = 24[/B] Substitute a = 24 into equation (1): d = 2(24) [B]d = 48 So Andrea is 24 years old and Dina is 48 years old[/B]
Distance Rate and Time
Solves for distance, rate, or time in the equation d=rt based on 2 of the 3 variables being known.
Divide 73 into two parts whose product is 402
Divide 73 into two parts whose product is 40 Our first part is x Our second part is 73 - x The product of the two parts is: x(73 - x) = 40 Multiplying through, we get: -x^2 + 73x = 402 Subtract 40 from each side, we get: -x^2 + 73x - 402 = 0 This is a quadratic equation. To solve this, we type it in our search engine, choose "solve Quadratic", and we get: [LIST=1] [*]x = [B]6[/B] [*]x = [B]67[/B] [/LIST]
Does (6,5) make the equation y = x true
Does (6,5) make the equation y = x true x =6 and y = 5, so we have: 5 = 6 which is [B]false. So no[/B], it does not make the equation True.
does the equation y= x/3 represent a direct variation? If so, state the value of k
does the equation y= x/3 represent a direct variation? If so, state the value of k [B]Yes[/B], it's a direct variation equation. We rewrite this as: y = 1/3 * x So k = 1/3, and y varies directly as x.
Does the point (0, 3) satisfy the equation y = x?
Does the point (0, 3) satisfy the equation y = x? Plug in our values of x = 0 and y = 3: 3 = 0 This is false, so the point (0,3) does [B]not satisfy[/B] the equation y = x
Does the point (2, 4) satisfy the equation y = 2x?
Does the point (2, 4) satisfy the equation y = 2x? Plug in x = 2 to y = 2x: y = 2(2) y = 4 [B]Yes, the point (2,4) satisfies the equation y = 2x[/B]
Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers
Dunder Mifflin will print business cards for $0.10 each plus setup charge of $15. Werham Hogg offers business cards for $0.15 each with a setup charge of $10. What numbers of business cards cost the same from either company Declare variables: [LIST] [*]Let b be the number of business cards. [/LIST] [U]Set up the cost function C(b) for Dunder Mifflin:[/U] C(b) = Cost to print each business card * b + Setup Charge C(b) = 0.1b + 15 [U]Set up the cost function C(b) for Werham Hogg:[/U] C(b) = Cost to print each business card * b + Setup Charge C(b) = 0.15b + 10 The phrase [I]cost the same[/I] means we set both C(b)'s equal to each other and solve for b: 0.1b + 15 = 0.15b + 10 Solve for [I]b[/I] in the equation 0.1b + 15 = 0.15b + 10 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 0.1b and 0.15b. To do that, we subtract 0.15b from both sides 0.1b + 15 - 0.15b = 0.15b + 10 - 0.15b [SIZE=5][B]Step 2: Cancel 0.15b on the right side:[/B][/SIZE] -0.05b + 15 = 10 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 15 and 10. To do that, we subtract 15 from both sides -0.05b + 15 - 15 = 10 - 15 [SIZE=5][B]Step 4: Cancel 15 on the left side:[/B][/SIZE] -0.05b = -5 [SIZE=5][B]Step 5: Divide each side of the equation by -0.05[/B][/SIZE] -0.05b/-0.05 = -5/-0.05 b = [B]100[/B]
During a recent season Miguel Cabrera and Mike Jacobs hit a combined total of 46 home runs. Cabrera
During a recent season Miguel Cabrera and Mike Jacobs hit a combined total of 46 home runs. Cabrera hit 6 more home runs than Jacobs how many home runs did each player hit Let c be Miguel Cabrera's home runs and j be Mike Jacobs home runs. We are given two equations: [LIST=1] [*]c + j = 46 [*]c = j + 6 [/LIST] Substitute (2) into (1) (j + 6) + j = 46 Combine like terms: 2j + 6 = 46 [URL='https://www.mathcelebrity.com/1unk.php?num=2j%2B6%3D46&pl=Solve']Plugging this into our equation calculator[/URL], we get [B]j = 20[/B]. Substitute this into equation (2), we have: c = 20 + 6 [B]c = 26 [/B] Therefore, Mike Jacobs hit 20 home runs and Miguel Cabrera hit 26 home runs.
During the 2016 christmas season,UPS had 14 employees retire, 122 employees were hired and 31 left d
During the 2016 christmas season,UPS had 14 employees retire, 122 employees were hired and 31 left due to illness. If UPS ended the year with 410 employees, how many did they have at the start of the season? Let x be the number of employees at the start of the season. We have: [LIST] [*]-14 since retiring is an employee loss [*]+122 hired since hiring is an employee gain [*]-31 since illness means a leave [/LIST] x - 14 + 122 - 31 = 410 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=x-14%2B122-31%3D410&pl=Solve']equation solver[/URL], we get: [B]x = 333[/B]
During the summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also wor
During the summer, you work 30 hours per week at a gas station and earn $8.75 per hour. You also work as a landscaper for $11 per hour and can work as many hours as you want. You want to earn a total of $400 per week. How many hours, t, must you work as a landscaper? [U]Calculate your gas station salary:[/U] Gas Station Salary = Hours Worked * Hourly Rate Gas Station Salary = 30 * $8.75 Gas Station Salary = $262.50 [U]Now subtract this from the desired weekly earnings of $400[/U] $400 - 262.50 = $137.50 The landscaper makes $11 per hour. And they want to make $137.50 from landscaping. So we have the following equation: 11t = 137.50 Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=11t%3D137.50&pl=Solve']equation calculator[/URL], and we get t = 12.5 hours.
Dwayne earn $6 for each hour of yard work. After doing a total of 3 hours of yard work, how much mon
Dwayne earn $6 for each hour of yard work. After doing a total of 3 hours of yard work, how much money will Dwayne have earned? We're given the hourly earnings equation below: Hourly Earnings = Hourly Rate * hours worked Hourly Earnings = $6 * 3 Hourly Earnings = [B]$18[/B]
Each calendar will selll for $5.00 each. Write an equation to model the total income,y, for selling
Each calendar will selll for $5.00 each. Write an equation to model the total income,y, for selling x calendars income (y) = Price * Quantity [B]y = 5x[/B]
each classroom at HCS has a total of 26 desks. After Mr. Sean pond ordered 75 new desks the total nu
each classroom at HCS has a total of 26 desks. After Mr. Sean pond ordered 75 new desks the total number of desks in the school was 543. How many classrooms does the school have? Let d be the number of desks per classroom. We're given an equation: 26d + 75 = 543 To solve for d, [URL='https://www.mathcelebrity.com/1unk.php?num=26d%2B75%3D543&pl=Solve']type this equation into our search engine[/URL] and we get: d = [B]18[/B]
Each piece of candy costs 25 cents. The cost of x pieces of candy is $2.00. Use variable x to transl
Each piece of candy costs 25 cents. The cost of x pieces of candy is $2.00. Use variable x to translate the above statements into algebraic equation. Our algebraic expression is: [B]0.25x = 2 [/B] To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.25x%3D2&pl=Solve']type it in our search engine[/URL] and we get: x = [B]8[/B]
Ellipses
Given an ellipse equation, this calculates the x and y intercept, the foci points, and the length of the major and minor axes as well as the eccentricity.
Emily is three years older than twice her sister Mary�s age. The sum of their ages is less than 30.
Emily is three years older than twice her sister Mary�s age. The sum of their ages is less than 30. What is the greatest age Mary could be? Let e = Emily's age and m = Mary's age. We have the equation e = 2m + 3 and the inequality e + m < 30 Substitute the equation for e into the inequality: 2m + 3 + m < 30 Add the m terms 3m + 3 < 30 Subtract 3 from each side of the inequality 3m < 27 Divide each side of the inequality by 3 to isolate m m < 9 Therefore, the [B]greatest age[/B] Mary could be is 8, since less than 9 [U]does not include[/U] 9.
Equation 2y+5x=40. Interprt the intercepts
Equation 2y+5x=40. Interprt the intercepts Y intercept is when X = 0 2y + 5(0) = 40 2y = 40 Divide each side by 2 [B]y = 20 [/B] X intercept is when Y = 0 2(0) + 5x = 40 5x = 40 Divide each side by 5 [B]x = 8[/B]
Equation and Inequalities
Solves an equation or inequality with 1 unknown variable and no exponents as well as certain absolute value equations and inequalities such as |x|=c and |ax| = c where a and c are constants. Solves square root, cube root, and other root equations in the form ax^2=c, ax^2 + b = c. Also solves radical equations in the form asqrt(bx) = c. Also solves open sentences and it will solve one step problems and two step equations. 2 step equations and one step equations and multi step equations
Equation of a Plane
Given three 3-dimensional points, this calculates the equation of a plane that contains those points.
Equation of Exchange
Solves for any of the 4 variables in the Equation of Exchange: money, velocity, price, quantity
eric is twice as old as Shawn. The sum of their ages is 33. How old is Shawn?
eric is twice as old as Shawn. The sum of their ages is 33. How old is Shawn? Let Eric's age be e. Let Shawn's age be s. We're given two equations: [LIST=1] [*]e = 2s [*]e + s = 33 [/LIST] Substitute equation (1) into equation (2) for e so we can solve for s: 2s + s = 33 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=2s%2Bs%3D33&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]11[/B]
Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, wh
Ethan has $9079 in his retirement account, and Kurt has $9259 in his. Ethan is adding $19per day, whereas Kurt is contributing $1 per day. Eventually, the two accounts will contain the same amount. What balance will each account have? How long will that take? Set up account equations A(d) where d is the number of days since time 0 for each account. Ethan A(d): 9079 + 19d Kurt A(d): 9259 + d The problems asks for when they are equal, and how much money they have in them. So set each account equation equal to each other: 9079 + 19d = 9259 + d [URL='https://www.mathcelebrity.com/1unk.php?num=9079%2B19d%3D9259%2Bd&pl=Solve']Typing this equation into our search engine[/URL], we get [B]d = 10[/B]. So in 10 days, both accounts will have equal amounts in them. Now, pick one of the account equations, either Ethan or Kurt, and plug in d = 10. Let's choose Kurt's since we have a simpler equation: A(10) = 9259 + 10 A(10) = $[B]9,269 [/B] After 10 days, both accounts have $9,269 in them.
Expand Master and Build Polynomial Equations
This calculator is the
ultimate expansion tool to multiply polynomials. It expands algebraic expressions listed below using all 26 variables (a-z) as well as negative powers to handle polynomial multiplication. Includes multiple variable expressions as well as outside multipliers.
Also produces a polynomial equation from a given set of roots (polynomial zeros). * Binomial Expansions c(a + b)x
* Polynomial Expansions c(d + e + f)x
* FOIL Expansions (a + b)(c + d)
* Multiple Parentheses Multiplications c(a + b)(d + e)(f + g)(h + i)
Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and
Explain the steps you would take to find an equation for the line perpendicular to 4x - 5y = 20 and sharing the same y-intercept Get this in slope-intercept form by adding 5y to each side: 4x - 5y + 5y = 5y + 20 Cancel the 5y's on the left side and we get: 5y + 20 = 4x Subtract 20 from each side 5y + 20 - 20 = 4x - 20 Cancel the 20's on the left side and we get: 5y = 4x - 20 Divide each side by 5: 5y/5 = 4x/5 - 4 y = 4x/5 - 4 So we have a slope of 4/5 to find our y-intercept, we set x = 0: y = 4(0)/5 - 4 y = 0 - 4 y = -4 If we want a line perpendicular to the line above, our slope will be the negative reciprocal: The reciprocal of 4/5 is found by flipping the fraction making the numerator the denominator and the denominator the numerator: m = 5/4 Next, we multiply this by -1: -5/4 So our slope-intercept of the perpendicular line with the same y-intercept is: [B]y = -5x/4 - 4[/B]
Exponential Growth
This solves for any 1 of the 4 items in the exponential growth equation or exponential decay equation, Initial Value (P), Ending Value (A), Rate (r), and Time (t).
ey/n + k = t for y
ey/n + k = t for y Let's take this literal equation in pieces: Subtract k from each side: ey/n + k - k = t - k Cancel the k's on the left side, we have: ey/n = t - k Now multiply each side by n: ney/n = n(t - k) Cancel the n's on the left side, we have: ey = n(t - k) Divide each side by e: ey/e = n(t - k)/e Cancel the e's on the left side, we have: [B]y = n(t - k)/e[/B]
f - g = 1/4b for b
f - g = 1/4b for b Multiply each side of the equation by 4 to remove the 1/4 and isolate b: 4(f - g) = 4/4b 4/4 = 1, so we have: b = [B]4(f - g)[/B] [I]the key to this problem was multiplying by the reciprocal of the constant[/I]
f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b
f(x)=a(b)^x and we know that f(3)=17 and f(7)=3156. what is the value of b Set up both equations with values When x = 3, f(3) = 17, so we have a(b)^3 = 17 When x = 7, f(7) = 3156, so we have a(b)^7 = 3156 Isolate a in each equation a = 17/(b)^3 a = 3156/(b)^7 Now set them equal to each other 17/(b)^3 = 3156/(b)^7 Cross Multiply 17b^7 = 3156b^3 Divide each side by b^3 17b^4 = 3156 Divide each side by 17 b^4 = 185.6471 [B]b = 3.6912[/B]
Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith?
Faith is 1/5 her mother's age. Their combined ages are 30. How old is faith? Let Faith's age be f. Let her mother's age be m. We're given: [LIST=1] [*]f = m/5 [*]f + m = 30 [/LIST] Rearrange (1) by cross-multiplying: m = 5f Substitute this into equation (2): f + 5f = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=f%2B5f%3D30&pl=Solve']Type this equation into our search engine[/URL] and we get: f = [B]5[/B]
Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them
Farmer Yumi has too many plants in her garden. If she starts out with 150 plants and is losing them at a rate of 4% each day, how long will it take for her to have 20 plants left? Round UP to the nearest day. We set up the function P(d) where d is the number of days sine she started losing plants: P(d) = Initial plants * (1 - Loss percent / 100)^d Plugging in our numbers, we get: 20 = 150 * (1 - 4/100)^d 20 = 150 * (1 - 0.04)^d Read left to right so it's easier to read: 150 * 0.96^d = 20 Divide each side by 150, and we get: 0.96^d = 0.13333333333 To solve this logarithmic equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=0.96%5Ed%3D0.13333333333&pl=Calculate']type it in our search engine[/URL] and we get: d = 49.35 The problem tells us to round up, so we round up to [B]50 days[/B]
Find 2 consecutive numbers such that the sum of twice the smaller number and 3 times the larger numb
Find 2 consecutive numbers such that the sum of twice the smaller number and 3 times the larger number is 73. Let x be the smaller number and y be the larger number. We are given: 2x + 3y = 73 Since the numbers are consecutive, we know that y = x + 1. Substitute this into our given equation: 2x + 3(x + 1) = 73 Multiply through: 2x + 3x + 3 = 73 Group like terms: 5x + 3 = 73 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3%3D73&pl=Solve']Type 5x + 3 = 73 into the search engine[/URL], and we get [B]x = 14[/B]. Our larger number is 14 + 1 = [B]15 [/B] Therefore, our consecutive numbers are[B] (14, 15)[/B]
Find 3 Even Integers with a sum of 198
Find 3 Even Integers with a sum of 198 Let x be the first even integer. Then y is the next, and z is the third even integer. [LIST=1] [*]y = x + 2 [*]z = x + 4 [*]x + y + z = 198 [/LIST] Substituting y and z into (3): x + x + 2 + x + 4 = 198 Group x terms 3x + 6 = 198 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B6%3D198&pl=Solve']equation solver[/URL], we get: [B]x = 64[/B] y = 64 + 2 [B]y= 66[/B] z = 64 + 4 [B]z = 68[/B]
Find a linear function f, given f(16)=-2 and f(-12)=-9. Then find f(0)
Find a linear function f, given f(16)=-2 and f(-12)=-9. Then find f(0). We've got 2 points: (16, -2) and (-12, -9) Calculate the slope (m) of this line using: m = (y2 - y1)/(x2 - x1) m = (-9 - -2)/(-12 - 16) m = -7/-28 m = 1/4 The line equation is denoted as: y = mx + b Let's use the first point (x, y) = (16, -2) -2 = 1/4(16) + b -2 = 4 + b Subtract 4 from each side, and we get: b = -6 So our equation of the line is: y = 1/4x - 6 The questions asks for f(0): y = 1/4(0) - 6 y = 0 - 6 [B]y = -6[/B]
Find an equation of the line containing the given pair of points (1,5) and (3,6)
Find an equation of the line containing the given pair of points (1,5) and (3,6). Using our[URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=5&slope=+2%2F5&xtwo=3&ytwo=6&pl=You+entered+2+points'] point slope calculator[/URL], we get: [B]y = 1/2x + 9/2[/B]
Find four consecutive odd numbers which add to 64
Find four consecutive odd numbers which add to 64. Let the first number be x. The next three numbers are: x + 2 x + 4 x + 6 Add them together to get 64: x + (x + 2) + (x + 4) + (x + 6) = 64 Group like terms: 4x + 12 = 64 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=4x%2B12%3D64&pl=Solve']equation calculator[/URL], we get: [B]x = 13[/B] The next 3 odd numbers are: x + 2 = 13 + 2 = 15 x + 4 = 13 + 4 = 17 x + 6 = 13 + 6 = 19 So the 4 consecutive odd numbers which add to 64 are: [B](13, 15, 17, 19)[/B]
Find r in P(7, r)
Find r in P(7, r) Recall the permutations formula: 7! / (7-r!) = 840. We [URL='https://www.mathcelebrity.com/factorial.php?num=7!&pl=Calculate+factorial']run 7! through our search engine[/URL] and we get: [URL='https://www.mathcelebrity.com/factorial.php?num=7!&pl=Calculate+factorial']7![/URL] = 5040 5040 / (7 - r)! = 840 Cross multiply, and we get: 5040/840 = 7 - r! 6 = (7 - r)! Since 6 = 3*2*! = 3!, we have; 3! = (7 - r)! 3 = 7 - r To solve for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=3%3D7-r&pl=Solve']type this equation into our search engine[/URL] and we get: r = [B]4[/B]
Find the gradient of the the line with the equation 8x - 4y =12
Find the gradient of the the line with the equation 8x - 4y =12 [URL='https://www.mathcelebrity.com/parperp.php?line1=8x-4y%3D12&line2=6x+-+3y+%3D+18&pl=Slope']Type this equation into our search engine[/URL] and choose "slope" and we get: Slope (gradient) = [B]2[/B]
Find two consecutive integers if the sum of their squares is 1513
Find two consecutive integers if the sum of their squares is 1513 Let the first integer be n. The next consecutive integer is (n + 1). The sum of their squares is: n^2 + (n + 1)^2 = 1513 n^2 + n^2 + 2n + 1 = 1513 2n^2 + 2n + 1 = 1513 Subtract 1513 from each side: 2n^2 + 2n - 1512 = 0 We have a quadratic equation. We [URL='https://www.mathcelebrity.com/quadratic.php?num=2n%5E2%2B2n-1512%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this into our search engine[/URL] and get: n = (-27, 28) Let's take the positive solution. The second integer is: n + 1 28 + 1 = 29
Find two consecutive odd integers such that the sum of their squares is 290
Find two consecutive odd integers such that the sum of their squares is 290. Let the first odd integer be n. The next odd integer is n + 2 Square them both: n^2 (n + 2)^2 = n^2 + 4n + 4 from our [URL='https://www.mathcelebrity.com/expand.php?term1=%28n%2B2%29%5E2&pl=Expand']expansion calculator[/URL] The sum of the squares equals 290 n^2 + n^2 + 4n + 4 = 290 Group like terms: 2n^2 + 4n + 4 = 290 [URL='https://www.mathcelebrity.com/quadratic.php?num=2n%5E2%2B4n%2B4%3D290&pl=Solve+Quadratic+Equation&hintnum=+0']Enter this quadratic into our search engine[/URL], and we get: n = 11, n = -13 Which means the two consecutive odd integer are: 11 and 11 + 2 = 13. [B](11, 13)[/B] -13 and -13 + 2 = -11 [B](-13, -11)[/B]
Find two consecutive positive integers such that the difference of their square is 25
Find two consecutive positive integers such that the difference of their square is 25. Let the first integer be n. This means the next integer is (n + 1). Square n: n^2 Square the next consecutive integer: (n + 1)^2 = n^2 + 2n + 1 Now, we take the difference of their squares and set it equal to 25: (n^2 + 2n + 1) - n^2 = 25 Cancelling the n^2, we get: 2n + 1 = 25 [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B1%3D25&pl=Solve']Typing this equation into our search engine[/URL], we get: n = [B]12[/B]
Find two consecutive positive integers such that the sum of their squares is 25
Find two consecutive positive integers such that the sum of their squares is 25. Let the first integer be x. The next consecutive positive integer is x + 1. The sum of their squares equals 25. We write this as:: x^2 + (x + 1)^2 Expanding, we get: x^2 + x^2 + 2x + 1 = 25 Group like terms: 2x^2 + 2x + 1 = 25 Subtract 25 from each side: 2x^2 + 2x - 24 = 0 Simplify by dividing each side by 2: x^2 + x - 12 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-12%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get x = 3 or x = -4. The problem asks for positive integers, so we discard -4, and use 3. This means, our next positive integer is 3 + 1 = 4. So we have [B](3, 4) [/B]as our answers. Let's check our work: 3^2 + 4^2 = 9 + 16 = 25
Find y if the line through (1, y) and (2, 7) has a slope of 4.
Find y if the line through (1, y) and (2, 7) has a slope of 4. Given two points (x1, y1) and (x2, y2), Slope formula is: slope = (y2 - y1)/(x2 - x1) Plugging in our coordinates and slope to this formula, we get: (7 - y)/(2 - 1) = 4 7 - y/1 = 4 7 - y = 4 To solve this equation for y, w[URL='https://www.mathcelebrity.com/1unk.php?num=7-y%3D4&pl=Solve']e type it in our search engine[/URL] and we get: y = [B]3[/B]
Fiona thinks of a number. fiona halves the number and gets an answer of 72.8. Form an equation with
Fiona thinks of a number. fiona halves the number and gets an answer of 72.8. Form an equation with x from the information Halving means dividing by 2, so our equation is: [B]x/2 = 72.8[/B]
Five times Kim's age plus 13 equals 58. How old is Kim?
Five times Kim's age plus 13 equals 58. How old is Kim? Let Kim's age be a. We have: Five times Kim's age: 5a Plus 13 means we add 13 5a + 13 Equals 58 means we set the expression 5a + 13 equal to 58 5a + 13 = 58 <-- This is our algebraic expression To solve this equation for a, [URL='https://www.mathcelebrity.com/1unk.php?num=5a%2B13%3D58&pl=Solve']we type it into our search engine[/URL] and get: a = [B]9[/B]
For g(x) = 4-5x, determine the input for x when the output of g(x) is -6
For g(x) = 4-5x, determine the input for x when the output of g(x) is -6 We want to know when: 4 - 5x = 6 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=4-5x%3D6&pl=Solve']type it in our search engine[/URL] and we get: x = [B]-0.4 or -2/5[/B]
for the function, h(x) = bx - 22, b is a constant and h(-5) = -7. Find the value of h(5)
for the function, h(x) = bx - 22, b is a constant and h(-5) = -7. Find the value of h(5) h(-5) = -5b - 22 Since we're given h(-5) = -7, we have: -5b - 22 = -7 [URL='https://www.mathcelebrity.com/1unk.php?num=-5b-22%3D-7&pl=Solve']Typing this equation into our search engine[/URL], we get: b = -3 So our h(x) equation is now: h(x) = -3x - 22 The problem asks for h(5): h(5) = -3(5) - 22 h(5) = 15 - 22 h(5) = [B]-37[/B]
Four-fifths of Kayla�s Math Notebook is filled. She has written on 48 pages. How many pages is there
Four-fifths of Kayla�s Math Notebook is filled. She has written on 48 pages. How many pages is there total in the notebook? Let the total pages be p. WE're given: 4p/5 = 48 To solve for p, we[URL='https://www.mathcelebrity.com/prop.php?num1=4p&num2=48&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value'] type this equation into our search engine[/URL] and we get: p = [B]60[/B]
Gabe rents a piano for $49 per month. He earns $15 per hour giving piano lessons to students. How ma
Gabe rents a piano for $49 per month. He earns $15 per hour giving piano lessons to students. How many hours of lessons per month must he give to earn a profit of $326? Build a profit function P(h) where h is the number of hours: P(h) = Hourly Rate * Number of Hours (h) - Cost of Piano P(h) = 15h - 49 The problem asks for the number of hours where P(h) = $326 15h - 49 = 326 We take this equation and [URL='https://www.mathcelebrity.com/1unk.php?num=15h-49%3D326&pl=Solve']type it in our search engine[/URL] to solve for h: h = [B]25[/B]
Gary has three less pets than Abe. If together they own 15 pets, how many pets does Gary own?
Let g = Gary's pets and a = Abe's pets. We are given two equations: (1) g = a - 3 (2) a + g = 15 Substitute (1) into (2) a + (a - 3) = 15 Combine Like Terms: 2a - 3 = 15 Add 3 to each side: 2a = 18 Divide each side by 2 to isolate a: a = 9 --> Abe has 9 pets Substitute a = 9 into Equation (1) g = 9 - 3 g = 6 --> Gary has 6 pets
Gayle has 36 coins, all nickels and dimes, worth $2.40. How many dimes does she have?
Gayle has 36 coins, all nickels and dimes, worth $2.40. How many dimes does she have? Set up our given equations using n as the number of nickels and d as the number of dimes: [LIST=1] [*]n + d = 36 [*]0.05n + 0.1d = 2.40 [/LIST] Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+d+%3D+36&term2=0.05n+%2B+0.1d+%3D+2.40&pl=Cramers+Method']simultaneous equations calculator[/URL] to get: n = 24 [B]d = 12[/B]
Geocache puzzle help
Let x equal the number of sticks he started with. We have: The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19 Add 0.2 to each side: 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2 Multiply each side by 5/4 (3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24 Multiply the inside piece first: 2/6x - 2/6 - 1/3 2/6x - 4/6 Now subtract 0.75 which is 3/4 2/6x - 4/6 - 3/4 4/6 is 8/12 and 3/4 is 9/12, so we have: 2/6x - 17/12 Now multiply by 3/4 6/24x - 51/48 = 24 Simplify: 1/4x - 17/16 = 24 Multiply through by 4 x - 17/4 = 96 Since 17/4 = 4.25, add 4.25 to each side x = 100.25 Since he did not cut up any sticks, he has a full stick to start with: So x = [B]101[/B]
Geocache puzzle help
Ok. To go further in this equation. It reads: ...How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Does that make sense to reverse 303? :-/ Thank you for your help!!
Geocache puzzle help
Ok. To go further in this equation. It reads: ...How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Does that make sense to reverse 303? :-/ Thank you for your help!!
Geocache puzzle help
Let x equal the number of sticks he started with. We have: The equation is 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) - 0.2 = 19 Add 0.2 to each side: 4/5 * (3/4 * (2/3 * (0.5x - 0.5) -1/3) - 0.75) = 19.2 Multiply each side by 5/4 (3/4 * (2/3 * (0.5x - 0.5) - 1/3) - 0.75) = 24 Multiply the inside piece first: 2/6x - 2/6 - 1/3 2/6x - 4/6 Now subtract 0.75 which is 3/4 2/6x - 4/6 - 3/4 4/6 is 8/12 and 3/4 is 9/12, so we have: 2/6x - 17/12 Now multiply by 3/4 6/24x - 51/48 = 24 Simplify: 1/4x - 17/16 = 24 Multiply through by 4 x - 17/4 = 96 Since 17/4 = 4.25, add 4.25 to each side x = 100.25 Since he did not cut up any sticks, he has a full stick to start with: So x = [B]101[/B]
Geocache puzzle help
Let me post the whole equation paragraph: Brainteaser # 1: Answer for ACH A fellow geocacher decided that he would try to sell some hand-made walking sticks at the local geocaching picnic event. In the first hour, he sold one-half of his sticks, plus one-half of a stick. The next hour, he sold one-third of his remaining sticks plus one-third of a stick. In the third hour, he sold one-fourth of what he had left, plus three-fourths of a stick. The last hour, he sold one-fifth of the remaining sticks, plus one-fifth of a stick. He did not cut up any sticks to make these sales. He returned home with 19 sticks. How many did he originally take to the event? Multiply the answer by 3 and reverse the digits. This will give you the answer for ACH in the coordinates. Make sure to multiply and reverse the digits. What would the answer be?
George has 600 baseball cards and Joy has one fifth as many baseball cards as George. How many baseb
George has 600 baseball cards and Joy has one fifth as many baseball cards as George. How many baseball cards does joy have? Let j = Joy's cards and g = George's cards. We have the following equation: g = 600 j = 1/5g So j = 600/5 [B]j = 120[/B]
George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a t
George has a certain number of apples, and Sarah has 4 times as many apples as George. They have a total of 25 apples. Let George's apples be g. Let Sarah's apples be s. We're give two equations: [LIST=1] [*]s = 4g [*]g + s = 25 [/LIST] Substitute equation (1) into equation (2) for s: g + 4g = 25 If [URL='https://www.mathcelebrity.com/1unk.php?num=g%2B4g%3D25&pl=Solve']we plug this equation into our search engine[/URL] and solve for g, we get: g = [B]5[/B] Now substitute this into equation 1 for g = 5: s = 4(5) s = [B]20[/B] [B]So George has 5 apples and Sarah has 20 apples[/B]
Georgie joins a gym. she pays $25 to sign up and then $15 each month. Create an equation using this
Georgie joins a gym. she pays $25 to sign up and then $15 each month. Create an equation using this information. Let m be the number of months Georgie uses the gym. Our equation G(m) is the cost Georgie pays for m months. G(m) = Variable Cost * m (months) + Fixed Cost Plug in our numbers: [B]G(m) = 15m + 25[/B]
Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2
Germany and Austria have a total of 25 states. Germany has 7 more states than Austria has. Create 2 equations. Let g be the number of German states. Let a be the number of Austrian states. We're given two equations: [LIST=1] [*]a + g = 25 [*]g = a + 7 [/LIST] To solve this system of equations, we substitute equation (2) into equation (1) for g: a + (a + 7) = 25 Combine like terms: 2a + 7 = 25 To solve for a, we[URL='https://www.mathcelebrity.com/1unk.php?num=2a%2B7%3D25&pl=Solve'] type this equation into our search engine[/URL] and we get: [B]a = 9[/B] To solve for g, we plug in a = 9 into equation (2): g = 9 + 7 [B]g = 16[/B]
Giovanni is thinking of a number. If he adds 2 to it, then divides that sum by 3, he gets 7. What is
Giovanni is thinking of a number. If he adds 2 to it, then divides that sum by 3, he gets 7. What is the number? Let the number be n: [LIST] [*]n [*]Add 2: n + 2 [*]Divide the sum by 3: (n + 2)/3 [*]The word "gets" means an equation, so we set (n + 2)/3 equal to 7 [/LIST] (n + 2)/3 = 7 Cross multiply: n + 2 = 21 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B2%3D21&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]19[/B]
Given f = cd^3, f = 450, and d = 10, what is c?
Given f = cd^3, f = 450, and d = 10, what is c? A) 0.5 B) 4.5 C) 15 D) 45 E) 150 Plugging in our numbers, we get: c(10)^3 = 450 Since 10^3 = 1000, we have: 1000c = 450 [URL='https://www.mathcelebrity.com/1unk.php?num=1000c%3D450&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]c = 0.45 Answer B[/B]
Given g(x)=-x-1, solve for x when g(x)=3
Given g(x)=-x-1, solve for x when g(x)=3 we have: -x - 1 = 3 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=-x-1%3D3&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]-4[/B]
Given the function f(x)=3x?9, what is the value of x when f(x)=9
Given the function f(x)=3x?9, what is the value of x when f(x)=9 Plug in our numbers and we get: 3x - 9 = 9 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=3x-9%3D9&pl=Solve']type it in our search engine[/URL] and we get: x = [B]6[/B]
Given: 9 - 4x = -19 Prove: x = 7
Given: 9 - 4x = -19 Prove: x = 7 Solve for [I]x[/I] in the equation 9 - 4x = - 19 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 9 and -19. To do that, we subtract 9 from both sides -4x + 9 - 9 = -19 - 9 [SIZE=5][B]Step 2: Cancel 9 on the left side:[/B][/SIZE] -4x = -28 [SIZE=5][B]Step 3: Divide each side of the equation by -4[/B][/SIZE] -4x/-4 = -28/-4 x = [B]7[/B]
Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking a
Graham is hiking at an altitude of 14,040 feet and is descending 50 feet each minute.Max is hiking at an altitude of 12,500 feet and is ascending 20 feet each minute. How many minutes will it take until they're at the same altitude? Set up the Altitude function A(m) where m is the number of minutes that went by since now. Set up Graham's altitude function A(m): A(m) = 14040 - 50m <-- we subtract for descending Set up Max's altitude function A(m): A(m) = 12500 + 20m <-- we add for ascending Set the altitudes equal to each other to solve for m: 14040 - 50m = 12500 + 20m [URL='https://www.mathcelebrity.com/1unk.php?num=14040-50m%3D12500%2B20m&pl=Solve']We type this equation into our search engine to solve for m[/URL] and we get: m = [B]22[/B]
Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older tha
Grandmother, mother and daughter are celebrating 150 years of life. The Mother is 25 years older than her daughter, but 31 years younger than her mother (the grandmother). How old are the three Let grandmother's age be g. Let mother's age be m. Let daughter's age be d. We're given 3 equations: [LIST=1] [*]m = d + 25 [*]m = g - 31 [*]d + g + m = 150 [/LIST] This means the daughter is: d = 25 + 31 = 56 years younger than her grandmother. So we have: 4. d = g - 56 Plugging in equation (2) and equation(4) into equation (3) we get: g - 56 + g + g - 31 Combine like terms: 3g - 87 = 150 [URL='https://www.mathcelebrity.com/1unk.php?num=3g-87%3D150&pl=Solve']Typing this equation into the search engine[/URL], we get: [B]g = 79[/B] Plug this into equation (2): m = 79 - 31 [B]m = 48[/B] Plug this into equation (4): d = 79 - 56 [B]d = 23[/B]
Gross Domestic Product (GDP)
Solves for all items of the Gross Domestic Product (GDP) equation:
GDP
Consumption (C)
Investment (I)
Government Spending (G)
Exports (X)
Imports (I).
Guadalupe left the restaurant traveling 12 mph. Then, 3 hours later, Lauren left traveling the same
Guadalupe left the restaurant traveling 12 mph. Then, 3 hours later, Lauren left traveling the same direction at 24 mph. How long will Lauren travel before catching up with Guadalupe? Distance = Rate x Time Guadulupe will meet Lauren at the following distance: 12t = 24(t - 3) 12t = 24t - 72 [URL='https://www.mathcelebrity.com/1unk.php?num=12t%3D24t-72&pl=Solve']Typing that equation into our search engine[/URL], we get: t = 6
Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think
Gym A: $75 joining fee and $35 monthly charge. Gym B: No joining fee and $60 monthly charge. (Think of the monthly charges paid at the end of the month.) Enter the number of months it will take for the total cost for both gyms to be equal. Gym A cost function C(m) where m is the number of months: C(m) = Monthly charge * months + Joining Fee C(m) = 35m + 75 Gym B cost function C(m) where m is the number of months: C(m) = Monthly charge * months + Joining Fee C(m) = 60m Set them equal to each other: 35m + 75 = 60m To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=35m%2B75%3D60m&pl=Solve']we type this equation into our search engine[/URL] and get: m = [B]3[/B]
Half of a pepperoni pizza plus 3/4ths of a ham and pineapple pizza has 765 calories. 1/4th of a pepp
Half of a pepperoni pizza plus 3/4ths of a ham and pineapple pizza has 765 calories. 1/4th of a pepperoni pizza and a whole ham and pineapple pizza contains 745 calories. How many calories are each of the 2 kinds of pizzas individually? Let p be the pepperoni pizza calories and h be the ham and pineapple pizza calories. We're given [LIST=1] [*]0.5p + 0.75h = 765 [*]0.25p + h = 745 [/LIST] With this system of equations, we can solve using 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.5p+%2B+0.75h+%3D+765&term2=0.25p+%2B+h+%3D+745&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.5p+%2B+0.75h+%3D+765&term2=0.25p+%2B+h+%3D+745&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.5p+%2B+0.75h+%3D+765&term2=0.25p+%2B+h+%3D+745&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [B]h = 580 p = 660[/B]
Hans rented a truck for one day. There was a base fee of 16.95, and there was an additional charge o
Hans rented a truck for one day. There was a base fee of 16.95, and there was an additional charge of 76 cents for each mile driven. Hans had to pay 152.99 when he returned the truck. For how many miles did he drive the truck? Set up the equation where x is the amount of miles he drove: 0.76x + 16.95 = 152.99 [URL='http://www.mathcelebrity.com/1unk.php?num=0.76x%2B16.95%3D152.99&pl=Solve']Plug this equation into our calculator[/URL]: x = 179 miles
Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $1
Happy Paws charges $16.00 plus $1.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $2.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours. Happy Paws Cost: C = 16 + 1.5h Woof Watchers: C = 11 + 2.75h Setup the equation where there costs are equal 16 + 1.5h = 11 + 2.75h Subtract 11 from each side: 5 + 1.5h = 2.75h Subtract 1.5h from each side 1.25h = 5 Divide each side by 1.25 [B]h = 4[/B]
Happy Paws charges $19.00 plus $5.50 per hour to keep a dog during the day. Woof Watchers charges $1
Happy Paws charges $19.00 plus $5.50 per hour to keep a dog during the day. Woof Watchers charges $11.00 plus $6.75 per hour. Complete the equation and solve it to find for how many hours the total cost of the services is equal. Use the variable h to represent the number of hours. [B]Happy Paws cost equation:[/B] 5.50h + 19 [B]Woof Watchers cost equation:[/B] 6.75h + 11 [B]Set them equal to each other:[/B] 5.50h + 19 = 6.75h + 11 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=5.50h%2B19%3D6.75h%2B11&pl=Solve']equation solver[/URL], we get [B]h = 6.4[/B].
He charges $1.50 per delivery and then $2 per km he has to drive to get from his kitchen to the deli
He charges $1.50 per delivery and then $2 per km he has to drive to get from his kitchen to the delivery address. Write an equation that can be used to calculate the delivery price and the distance between the kitchen and the delivery address. Use your equation to calculate the total cost to deliver to someone 2.4km away Let k be the number of kilometers between the kitchen and delivery address. Our Delivery equation D(k) is: [B]D(k) = 2k + 1.50[/B] The problem wants to know D(2.4): D(2.4) = 2(2.4) + 1.50 D(2.4) = 4.8 + 1.50 D(2.4) = [B]$6.30[/B]
heat loss of a glass window varies jointly as the window's area and the difference between the outsi
heat loss of a glass window varies jointly as the window's area and the difference between the outside and the inside temperature. a window 6 feet wide by 3 feet long loses 1,320 btu per hour when the temperature outside is 22 degree colder than the temperature inside. Find the heat loss through a glass window that is 3 feet wide by 5 feet long when the temperature outside is 9 degree cooler than the temperature inside. Find k of the equation: 6*3*22*k = 1320 396k = 1,320 k = 3.33333 [URL='https://www.mathcelebrity.com/1unk.php?num=396k%3D1320&pl=Solve']per our equation solver[/URL] Now, find the heat loss for a 3x5 window when the temperature is 9 degrees cooler than the temperature inside: 3*5*9*3.333333 = [B]450 btu per hour[/B]
Help on problem
[B]I need 36 m of fencing for my rectangular garden. I plan to build a 2m tall fence around the garden. The width of the garden is 6 m shorter than twice the length of the garden. How many square meters of space do I have in this garden? List the answer being sought (words) ______Need_________________________ What is this answer related to the rectangle?_Have_________________________ List one piece of extraneous information____Need_________________________ List two formulas that will be needed_______Have_________________________ Write the equation for width_____________Have_________________________ Write the equation needed to solve this problem____Need____________________[/B]
Help on problem
[B]List the answer being sought (words) ______Area of the garden What is this answer related to the rectangle?_Have_________________________ List one piece of extraneous information____2m tall fence List two formulas that will be needed_______P = 36. P = 2l + 2w Write the equation for width_____________w = 2l - 6 Write the equation needed to solve this problem A = lw, P = 2l + 2w[/B]
Help Plz
There are three siblings in a family. Their ages add to 26. Let nicks age be "x". John in half of micks age and Pip is two thirds of johns age. write an equation and solve. Find each Childs age.
Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took
Henrietta hired a tutor to help her improve her math scores. While working with the tutor, she took four tests. She scored 10 points better on the second test than she did on the first, 20 points better on the third test than on the first, and 30 points better on the fourth test than on the first. If the mean of these four tests was 70, what was her score on the third test? Givens: [LIST] [*]Let the first test score be s: [*]The second test score is: s + 10 [*]The third test score is: s + 20 [*]The fourth test score is: s + 30 [/LIST] The mean of the four tests is 70, found below: Sum of test scores / Number of Tests = Mean Plugging in our number, we get: (s + s + 10 + s + 20 + s + 30) / 4 = 70 Cross multiply and simplify: 4s + 60 = 70 * 4 4s + 60 = 280 To [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B60%3D280&pl=Solve']solve this equation for s, we type it in our search engine[/URL] and we get: s = 55 So the third test score: s + 20 = 55 + 20 [B]75[/B]
Hope it's okay to ask this here?
a) 1800 is the cost to run the business for a day. To clarify, when you plug in x = 0 for 0 candy bars sold, you are left with -1,800, which is the cost of doing business for one day. b) Maximum profit is found by taking the derivative of the profit equation and setting it equal to 0. P'(x) = -0.002x + 3 With P'(x) = 0, we get: -0.002x + 3 = 0 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=-0.002x%2B3%3D0&pl=Solve']equation solver[/URL], we get: x = 1,500 To get maximum profit, we plug in x = 1,500 to our [I]original profit equation[/I] P(1,500) = ? 0.001(1,500)^2 + 3(1,500) ? 1800 P(1,500) = -2,250 + 4,500 - 1,800 P(1,500) = $[B]450[/B]
How long will it take $3000 to earn $900 interest at 6% simple interest?
How long will it take $3000 to earn $900 interest at 6% simple interest? Set up the simple interest equation for the interest piece: 3000 * 0.06t = 900 To solve for t in this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=3000%2A0.06t%3D900&pl=Solve']type it in our search engine [/URL]and we get: t = [B]5[/B]
How many dimes must be added to a bag of 200 nickels so that the average value of the coins in the b
How many dimes must be added to a bag of 200 nickels so that the average value of the coins in the bag is 8 cents? 200 nickels has a value of 200 * 0.05 = $10. Average value of coins is $10/200 = 0.05 Set up our average equation, where we have total value divided by total coins: (200 * 0.05 + 0.1d)/(200 + d) = 0.08 Cross multiply: 16 + 0.08d = 10 + 0.1d Using our [URL='http://www.mathcelebrity.com/1unk.php?num=16%2B0.08d%3D10%2B0.1d&pl=Solve']equation solver[/URL], we get: [B]d = 300[/B]
How many twelfths equal three-sixths?
How many twelfths equal three-sixths? We set up the equation below where x is the number of twelfths in three-sixths: 1/12x = 3/6 Cross multiply, and we get: 12x * 3 = 6 * 1 36x = 6 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=36x%3D6&pl=Solve']type this in our math engine[/URL] and we get: x = [B]1/6 or 0.16667[/B]
How much money must be invested to accumulate $10,000 in 8 years at 6% compounded annually?
How much money must be invested to accumulate $10,000 in 8 years at 6% compounded annually? We want to know the principle P, that accumulated to $10,000 in 8 years compounding at 6% annually. [URL='https://www.mathcelebrity.com/simpint.php?av=10000&p=&int=6&t=8&pl=Compound+Interest']We plug in our values for the compound interest equation[/URL] and we get: [B]$6,274.12[/B]
How much would you need to deposit in an account now in order to have $6000 in the account in 10 yea
How much would you need to deposit in an account now in order to have $6000 in the account in 10 years? Assume the account earns 6% interest compounded monthly. We start with a balance of B. We want to know: B(1.06)^10 = 6000 B(1.79084769654) = 6000 Divide each side of the equation by 1.79084769654 to solve for B B = [B]3,350.37[/B]
How old am I if 400 reduced by 2 times my age is 244?
How old am I if 400 reduced by 2 times my age is 244? Let my age be a. We're given: 400 - 2a = 244 To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D244&pl=Solve']type this equation into our search engine [/URL]and we get: a = [B]78[/B]
How old am I if 400 reduced by 3 times my age is 124?
How old am I if 400 reduced by 3 times my age is 124? Let my age be a. We're given an algebraic expression: [LIST] [*]3 times my age means we multiply a by 3: 3a [*]400 reduced by 3 times my age means we subtract 3a from 400: [*]400 - 3a [*]The word [I]is[/I] mean an equation, so we set 400 - 3a equal to 124 [/LIST] 400 - 3a = 124 To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=400-3a%3D124&pl=Solve']we type this equation into our search engine[/URL] and we get: a = [B]92[/B]
How old am I if: 210 reduced by 3 times my current age is 4 times my current age?
How old am I if: 210 reduced by 3 times my current age is 4 times my current age? Let your current age be a. We're given: [LIST] [*]210 reduced by 3 times current age = 210 - 3a [*]4 times current age = 4a [*]The word [I]is[/I] means equal to. So we set 210 - 3a equal to 4a [/LIST] 210 - 3a = 4a To solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=210-3a%3D4a&pl=Solve']type this equation into our search engine [/URL]and we get: a = [B]30[/B]
How old am I of 400 reduced by 2 times my age is 224
How old am I of 400 reduced by 2 times my age is 224 [LIST=1] [*]Let my age be a. [*]2 times my age: 2a [*]400 reduced by 2 times my age: 400 - 2a [*]The phrase [I]is [/I]means an equation. So we set 400 - 2a equal to 224 for our algebraic expression [/LIST] [B]400 - 2a = 224 [/B] If the problem asks you to solve for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=400-2a%3D224&pl=Solve']type this equation into our search engine[/URL] and we get: a = [B]88[/B]
Hyperbola
Given a hyperbola equation, this calculates:
* Equation of the asymptotes
* Intercepts
* Foci (focus) points
* Eccentricity ε
* Latus Rectum
* semi-latus rectum
I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5
I am thinking of a number. I multiply it by 14 and add 13. I get the same answer if I multiply by 5 and add 283. What is my number? Let the number be n. We're given two expressions: [LIST=1] [*]Multiply it by 14 and add 13: 14n + 13 [*]Multiply by 5 and add 283: 5n + 283 [/LIST] The phrase [I]I get the same answer[/I] means an equation. So we set expression 1 equal to expression 2: 14n + 13 = 5n + 283 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B13%3D5n%2B283&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]30[/B]
I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4
I am thinking of a number. I multiply it by 14 and add 21. I get the same answer if I multiply by 4 and add 141. Let the number be n. We have two expressions: [LIST=1] [*]Multiply by 14 and add 21 is written as: 14n + 21 [*]Multiply by 4 and add 141 is written as: 4n + 141 [/LIST] The phrase [I]get the same expression[/I] means they are equal. So we set (1) and (2) equal to each other and solve for n: 14n + 21 = 4n + 141 [URL='https://www.mathcelebrity.com/1unk.php?num=14n%2B21%3D4n%2B141&pl=Solve']Type this equation into our search engine [/URL]to solve for n and we get: n = [B]12[/B]
I am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 s
I am Thinking of a number. I multiply it by 3 and add 67. I get the same answer If i multiply by 6 subtract 8. Let the number be n. We're given two equal expressions: [LIST=1] [*]3n + 67 [*]6n - 8 [/LIST] Set the expressions equal to each other since they give the [B]same answer[/B]: 3n + 67 = 6n - 8 We have an equation. [URL='https://www.mathcelebrity.com/1unk.php?num=3n%2B67%3D6n-8&pl=Solve']Type this equation into our search engine and we get[/URL]: n = [B]25[/B]
I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 a
I am thinking of a number. I multiply it by 7 and add 25. I get the same answer if I multiply by 3 and add 93. What is my number? Let the number be n. We're given two expressions: [LIST] [*]Multiply the number by 7: 7n [*]add 25: 7n + 25. <-- Expression 1 [*]Multiply by 3: 3n [*]Add 93: 3n + 93 <-- Expression 2 [*]The phrase [I]get the same answer[/I] means both expression 1 and expression 2 are equal. So we set them equal to each other: [/LIST] 7n + 25 = 3n + 93 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=7n%2B25%3D3n%2B93&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]17[/B]
I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13
I am thinking of a number.i multiply it by 5 and add 139. I get the same number if I multiply by 13 and subtract 13.What is my number? Take a number (n): The first operation is multiply 5 times n, and then add 39: 5n + 139 The second operation is multiply 13 times n and subtract 13: 13n - 13 Set both operations equal to each other since they result in [I]the same number[/I] 5n + 139 = 13n - 13 [URL='https://www.mathcelebrity.com/1unk.php?num=5n%2B139%3D13n-13&pl=Solve']Type this equation into our search engine[/URL] and we get: [B]n = 19[/B]
I HAVE $11.60, all dimes and quarters, in my pocket. I have 32 more dimes than quarters. how many di
I HAVE $11.60, all dimes and quarters, in my pocket. I have 32 more dimes than quarters. how many dimes, and how many quarters do i have? Let d = dimes and q = quarters. We have two equations: [LIST=1] [*]0.10d + 0.25q = 11.60 [*]d - q = 32 [/LIST] Set up a [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=0.10d+%2B+0.25q+%3D+11.60&term2=d+-+q+%3D+32&pl=Cramers+Method']system of equations[/URL] to solve for d and q. [B]dimes (d) = 56 and quarters (q) = 24[/B] Check our work: 56 - 24 = 32 0.10(56) + 0.25(24) = $5.60 + $6.00 = $11.60
I have 20 bills consisting of $5 and $10. If the total amount of my money is $130, how many of each
I have 20 bills consisting of $5 and $10. If the total amount of my money is $130, how many of each bill do i have? Let f be $5 bills and t be $10 bills, we have: f + t = 20 5f + 10t = 130 Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=f%2Bt%3D20&term2=5f+%2B+10t+%3D+130&pl=Cramers+Method']system of equation solver[/URL], we get: [LIST] [*][B]f = 14[/B] [*][B]t = 6[/B] [/LIST]
I have saved 24 to buy a game which is three-fourth of the total cost of the game how much does the
I have saved 24 to buy a game which is three-fourth of the total cost of the game how much does the game cost ? Let the cost of the game be c. We're given: 3c/4 = 24 To solve this equation for c, we [URL='https://www.mathcelebrity.com/prop.php?num1=3c&num2=24&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our search engine[/URL] and we get: c = [B]32[/B]
I only own blue blankets and red blankets. 8 out of every 15 blankets I have are red.
I only own blue blankets and red blankets. 8 out of every 15 blankets I have are red. If have i 45 blankets, how many are blue? If 8 out of 15 blankets are red, then 15 - 8 = 7 are blue So 7 out of every 15 blankets are blue. Set up a proportion of blue blankets to total blankets where b is the number of blue blankets in 45 blankets 7/15 = b/45 Cross multiply: If 2 proportions are equal, then we can do the following: Numerator 1 * Denominator 2 = Denominator 1 * Numerator 2 15b = 45 * 7 15b = 315 To solve for b, divide each side of the equation by 15: 15b/15 = 315/15 Cancel the 15's on the left side and we get: b = [B]21[/B]
I think of a number. I multiply it by 6 and add 3. If my answer is 75, calculate the number I starte
I think of a number. I multiply it by 6 and add 3. If my answer is 75, calculate the number I started with. Let the number be n. Multiply it by 6: 6n Add 3: 6n + 3 If the answer is 75, we set 6n + 3 equal to 75: 6n + 3 = 75 We have an equation. To solve for n, [URL='https://www.mathcelebrity.com/1unk.php?num=6n%2B3%3D75&pl=Solve']we type this equation into our search engine[/URL] and get: [B]n = 12[/B]
If (x - 1)/3 = k and k = 2, what is the value of x?
If (x - 1)/3 = k and k = 2, what is the value of x? If k = 2, we have: (x - 1)/3 = 2 Cross multiply: x - 1 = 3 * 2 x - 1 = 6 [URL='https://www.mathcelebrity.com/1unk.php?num=x-1%3D6&pl=Solve']Type this equation into the search engine[/URL], we get: [B]x = 7[/B]
If 1/2 cup of milk makes 8 donuts. How much cups it takes to make 28 donuts
If 1/2 cup of milk makes 8 donuts. How much cups it takes to make 28 donuts? Set up a proportion of cups to donuts, where c is the number of cups required to make 28 donuts: 1/2/8 = c/28 Cross multiply: 28(1/2) = 8c 8c = 14 [URL='https://www.mathcelebrity.com/1unk.php?num=8c%3D14&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]c = 1.75[/B]
If 100 runners went with 4 bicyclists and 5 walkers, how many bicyclists would go with 20 runners an
If 100 runners went with 4 bicyclists and 5 walkers, how many bicyclists would go with 20 runners and 2 walkers? [U]Set up a joint variation equation, for the 100 runners, 4 bicyclists, and 5 walkers:[/U] 100 = 4 * 5 * k 100 = 20k [U]Divide each side by 20[/U] k = 5 <-- Coefficient of Variation [U]Now, take scenario 2 to determine the bicyclists with 20 runners and 2 walkers[/U] 20 = 2 * 5 * b 20 = 10b [U]Divide each side by 10[/U] [B]b = 2[/B]
If 11 times a number is added to twice the number, the result is 104
If 11 times a number is added to twice the number, the result is 104 Let [I]the number[/I] be an arbitrary variable we call x. 11 times a number: 11x Twice the number (means we multiply x by 2): 2x The phrase [I]is added to[/I] means we add 2x to 11x: 11x + 2x Simplify by grouping like terms: (11 + 2)x = 13x The phrase [I]the result is[/I] means an equation, so we set 13x equal to 104: 13x = 104 <-- This is our algebraic expression To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=13x%3D104&pl=Solve']we type it in our search engine[/URL] and we get: x = [B]8[/B]
If 115% of a number is 460, what is 75% of the number
If 115% of a number is 460, what is 75% of the number. Let the number be n. We're given: 115% * n = 460 We write 115% of n as 1.15n, so we have: 1.15n = 460 [URL='https://www.mathcelebrity.com/1unk.php?num=1.15n%3D460&pl=Solve']Using our equation calculator[/URL], we get: n = [B]400 [/B] The problem asks for 75% of this number, so we [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=75&den1=400&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']type in [I]75% of 400[/I] into our search engine[/URL] and get: [B]300[/B]
If 12 times a number is added to twice the number, the result is 112
If 12 times a number is added to twice the number, the result is 112. Let the number be n, so we have: 12n + 2n = 112 Combine like terms 14n = 112 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=14n%3D112&pl=Solve']equation solver[/URL], we get [B]n = 8[/B].
If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numer
If 2 is added to the numerator and denominator it becomes 9/10 and if 3 is subtracted from the numerator and denominator it become 4/5. Find the fractions. Convert 2 to a fraction with a denominator of 10: 20/2 = 10, so we multiply 2 by 10/10: 2*10/10 = 20/10 Add 2 to the numerator and denominator: (n + 2)/(d + 2) = 9/10 Cross multiply and simplify: 10(n + 2) = 9(d + 2) 10n + 20 = 9d + 18 Move constants to right side by subtracting 20 from each side and subtracting 9d: 10n - 9d = -2 Subtract 3 from the numerator and denominator: (n - 3)/(d - 3) = 4/5 Cross multiply and simplify: 5(n - 3) = 4(d - 3) 5n - 15 = 4d - 12 Move constants to right side by adding 15 to each side and subtracting 4d: 5n - 4d = 3 Build our system of equations: [LIST=1] [*]10n - 9d = -2 [*]5n - 4d = 3 [/LIST] Multiply equation (2) by -2: [LIST=1] [*]10n - 9d = -2 [*]-10n + 8d = -6 [/LIST] Now add equation (1) to equation (2) (10 -10)n (-9 + 8)d = -2 - 6 The n's cancel, so we have: -d = -8 Multiply through by -1: d = 8 Now bring back our first equation from before, and plug in d = 8 into it to solve for n: 10n - 9d = -2 10n - 9(8) = -2 10n - 72 = -2 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=10n-72%3D-2&pl=Solve']plug this equation into our search engine[/URL] and we get: n = 7 So our fraction, n/d = [B]7/8[/B]
If 25% of 30% of x is 9, what is x?
If 25% of 30% of x is 9, what is x? Convert percentages to decimals when multiplying: 25% = 0.25 30% = 0.3 0.25 * 0.3 * x = 9 0.075x = 9 Using our math engine, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.075x%3D9&pl=Solve']type this equation in[/URL] and we get: x = [B]120 [MEDIA=youtube]5EwNxiBdLu0[/MEDIA][/B]
If 25% of a number b is 25.18. What is 20% of b?
If 25% of a number b is 25.18. What is 20% of b? Using our 25% as 0.25, we have: 0.25b = 25.18 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=0.25x%20%3D%2025.18&pl=Solve']equation calculator[/URL], we get: b = 100.72 The question asks what is [URL='https://www.mathcelebrity.com/perc.php?num=+5&den=+8&num1=+16&pct1=+80&pct2=20&den1=100.72&pcheck=3&pct=+82&decimal=+65.236&astart=+12&aend=+20&wp1=20&wp2=30&pl=Calculate']20% of 100.72[/URL]. Using our calculator, we get: [B]20.144[/B]
If 3(c + d) = 5, what is the value of c + d?
If 3(c + d) = 5, what is the value of c + d? A) 3/5 B) 5/3 C) 3 D) 5 Divide each side of the equation by 3 to [U]isolate[/U] c + d 3(c + d)/3 = 5/3 Cancel the 3's on the left side, we get: c + d = [B]5/3, or answer B[/B]
if 30% of 40% of x is 18.6, find the value of x
if 30% of 40% of x is 18.6, find the value of x 30% is 0.3 40% is 0.4 So we have: 0.3 * 0.4 * x = 18.6 Simplifying, we get: 0.12x = 18.6 [URL='https://www.mathcelebrity.com/1unk.php?num=0.12x%3D18.6&pl=Solve']Typing this equation into our search engine[/URL], we get: x = [B]155[/B]
If 3r = 18, what is the value of 6r + 3?
If 3r = 18, what is the value of 6r + 3? A) 6 B) 27 C) 36 D) 39 If [URL='https://www.mathcelebrity.com/1unk.php?num=3r%3D18&pl=Solve']we type in the equation 3r = 18 into our search engine[/URL], we get: r = 6 Take r = 6, and subtitute it into 6r + 3: 6(6) + 3 36 + 3 [B]39, or answer D[/B]
If 4 times a number is added to 9, the result is 49
If 4 times a number is added to 9, the result is 49. [I]A number[/I] means an arbitrary variable, let's call it x. 4 [I]times a number[/I] means we multiply x by 4 4x [I]Added to[/I] 9 means we add 9 to 4x 4x + 9 [I]The result is[/I] means we have an equation, so we set 4x + 9 equal to 49 [B]4x + 9 = 49[/B] <-- This is our algebraic expression To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=4x%2B9%3D49&pl=Solve']we type it in the search engine[/URL] and get x = 10
If 4(x-9)=3x-8x, what is x?
[SIZE=5]If 4(x-9)=3x-8x, what is x? [/SIZE] [SIZE=4]Multiply through: 4x - 36 = 3x - 8x Group like terms: 4x - 36 = -5x [/SIZE] [URL='https://www.mathcelebrity.com/1unk.php?num=4x-36%3D-5x&pl=Solve'][SIZE=4]Typing this equation into the search[/SIZE][/URL][SIZE=4][URL='https://www.mathcelebrity.com/1unk.php?num=4x-36%3D-5x&pl=Solve'] engine[/URL], we get: [B]x = 4[/B][/SIZE]
If 4x+7=xy-6, then what is the value of x, in terms of y
If 4x+7=xy-6, then what is the value of x, in terms of y Subtract xy from each side: 4x + 7 - xy = -6 Add 7 to each side: 4x - xy = -6 - 7 4x - xy = -13 Factor out x: x(4 - y) = -13 Divide each side of the equation by (4 - y) [B]x = -13/(4 - y)[/B]
If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integ
If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integer. [LIST] [*]Let the integer be "x". [*]Square the integer: x^2 [*]7 times the square: 7x^2 [*]5 times the integer: 5x [*]Add them together: 7x^2 + 5x [*][I]The result is[/I] means an equation, so we set 7x^2 + 5x equal to 2 [/LIST] 7x^2 + 5x = 2 [U]This is a quadratic equation. To get it into standard form, we subtract 2 from each side:[/U] 7x^2 + 5x - 2 = 2 - 2 7x^2 + 5x - 2 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=7x%5E2%2B5x-2%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Type this problem into our search engine[/URL], and we get two solutions: [LIST=1] [*]x = 2/7 [*]x= -1 [/LIST] The problem asks for an integer, so our answer is x[B] = -1[/B]. [U]Let's check our work by plugging x = -1 into the quadratic:[/U] 7x^2 + 5x - 2 = 0 7(-1)^2 + 5(-1) - 2 ? 0 7(1) - 5 - 2 ? 0 0 = 0 So we verified our answer, [B]x = -1[/B].
If 72 is added to a number it will be 4 times as large as it was originally
If 72 is added to a number it will be 4 times as large as it was originally The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. x 72 added to a number: x + 72 4 times as large as it was originally means we take the original number x and multiply it by 4: 4x Now, the phrase [I]it will be[/I] means an equation, so we set x + 72 equal to 4x to get our final algebraic expression: [B]x + 72 = 4x[/B] [B][/B] If the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B72%3D4x&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]24[/B]
If 800 feet of fencing is available, find the maximum area that can be enclosed.
If 800 feet of fencing is available, find the maximum area that can be enclosed. Perimeter of a rectangle is: 2l + 2w = P However, we're given one side (length) is bordered by the river and the fence length is 800, so we have: So we have l + 2w = 800 Rearranging in terms of l, we have: l = 800 - 2w The Area of a rectangle is: A = lw Plug in the value for l in the perimeter into this: A = (800 - 2w)w A = 800w - 2w^2 Take the [URL='https://www.mathcelebrity.com/dfii.php?term1=800w+-+2w%5E2&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']first derivative[/URL]: A' = 800 - 4w Now set this equal to 0 for maximum points: 4w = 800 [URL='https://www.mathcelebrity.com/1unk.php?num=4w%3D800&pl=Solve']Typing this equation into the search engine[/URL], we get: w = 200 Now plug this into our perimeter equation: l = 800 - 2(200) l = 800 - 400 l = 400 The maximum area to be enclosed is; A = lw A = 400(200) A = [B]80,000 square feet[/B]
If 9 is added to 1/3 of a number, the result is 15. What is the number?
If 9 is added to 1/3 of a number, the result is 15. What is the number? The phrase [I]a number[/I] means an arbitrary variable, let's call it x: x 1/3 of a number means we multiply x by 1/3: x/3 9 is added to 1/3 of a number: x/3 + 9 The phrase [I]the result is[/I] means an equation. so we set x/3 + 9 equal to 15 x/3 + 9 = 15 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2F3%2B9%3D15&pl=Solve']type it in our search engine[/URL] and we get: x = [B]18[/B]
if 9 times a number is decreased by 6, the result is 111
if 9 times a number is decreased by 6, the result is 111 A number means an arbitrary variable, let's call it x. 9 times a number: 9x Decreased by 6 9x - 6 The result is 11, this means we set 9x - 6 equal to 11 [B]9x - 6 = 11 [/B] To solve this equation for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=9x-6%3D11&pl=Solve']equation calculator[/URL]
If a machine produces 100 bags per minute how long will it take to make 40,000
If a machine produces 100 bags per minute how long will it take to make 40,000 100 bags/ per minute = 40,000 bags / m Cross multiply 100m = 40000 [URL='https://www.mathcelebrity.com/1unk.php?num=100m%3D40000&pl=Solve']Type this equation into the search engine[/URL] and we get: m = [B]400[/B]
if a number is added to its square, it equals 20
if a number is added to its square, it equals 20. Let the number be an arbitrary variable, let's call it n. The square of the number means we raise n to the power of 2: n^2 We add n^2 to n: n^2 + n It equals 20 so we set n^2 + n equal to 20 n^2 + n = 20 This is a quadratic equation. So [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn%3D20&pl=Solve+Quadratic+Equation&hintnum=+0']we type this equation into our search engine[/URL] to solve for n and we get two solutions: [B]n = (-5, 4)[/B]
if a number is added to its square, the result is 72. find the number
if a number is added to its square, the result is 72. find the number. Let the number be n. We're given: n + n^2 = 72 Subtract 72 from each side, we get: n^2 + n - 72 = 0 This is a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-72%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this equation into our search engine[/URL], and we get: [B]n = 8 and n = -9[/B]
If a number is increased by 16 and then divided by 3, the result is 8
If a number is increased by 16 and then divided by 3, the result is 8. Let x be the number. We have: (x + 16)/3 = 8 Cross multiply x + 16 = 24 Using our equation calculator, we get: [B]x = 8[/B]
if a number is tripled the result is 60
if a number is tripled the result is 60 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x Triple the number means we multiply by 3: 3x The phrase [I]the result is[/I] means an equation, so we set 3x equal to 60: [B]3x = 60 <-- This is our algebraic expression [/B] If you want to solve this equation, then [URL='https://www.mathcelebrity.com/1unk.php?num=3x%3D60&pl=Solve']you type in 3x = 60 into the search engine[/URL] and get: x = 20
if a train travels at 80 mph for 15 mins, what is the distance traveled?
if a train travels at 80 mph for 15 mins, what is the distance traveled? Let d = distance, r = rate, and t = time, we have the distance equation: D = rt Plugging in our values for r and t, we have: D = 80mph * 15 min Remember our speed is in miles per hour, so 15 min equal 1/4 of an hour D = 80mph * 1/4 D = [B]20 miles[/B]
If Bill's salary is $25 and he gets a 20� commission on every newspaper he sells, how many must he s
If Bill's salary is $25 and he gets a 20� commission on every newspaper he sells, how many must he sell to make $47 Set up bills Earnings function E(n) where n is the number of newspapers he sells: E(n) =. Cost per newspaper * number of newspapers sold + base salary E(n) = 0.2n + 25 We're asked to find n when E(n) = 47, so we set E(n) = 47 and solve for n: 0.2n + 25 = 47 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=0.2n%2B25%3D47&pl=Solve']equation solver[/URL], we get: n = [B]110[/B]
If Ef = 3x,Fg = 2x,and EG = 5
If Ef = 3x,Fg = 2x,and EG = 5 By segment addition, we have: EF + FG = EG 3x + 2x = 5 To solve for x, we t[URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B2x%3D5&pl=Solve']ype this equation into our math engine [/URL]and we get: x = 1 So EF = 3(1) = [B]3[/B] FG = 2(1) = [B]2[/B]
If EF = 7x , FG = 3x , and EG = 10 , what is EF?
If EF = 7x , FG = 3x , and EG = 10 , what is EF? By segment addition: EF + FG = EG 7x + 3x = 10 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=7x%2B3x%3D10&pl=Solve']type it in our search engine[/URL] and we get: x = 1 Evaluating EF = 7x with x = 1, we get: EF = 7 * 1 EF = [B]7[/B]
If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG?
If EF = 9x - 17, FG = 17x - 14, and EG = 20x + 17, what is FG? By segment addition, we know that: EF + FG = EG Substituting in our values for the 3 segments, we get: 9x - 17 + 17x - 14 = 20x + 17 Group like terms and simplify: (9 + 17)x + (-17 - 14) = 20x - 17 26x - 31 = 20x - 17 Solve for [I]x[/I] in the equation 26x - 31 = 20x - 17 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 26x and 20x. To do that, we subtract 20x from both sides 26x - 31 - 20x = 20x - 17 - 20x [SIZE=5][B]Step 2: Cancel 20x on the right side:[/B][/SIZE] 6x - 31 = -17 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants -31 and -17. To do that, we add 31 to both sides 6x - 31 + 31 = -17 + 31 [SIZE=5][B]Step 4: Cancel 31 on the left side:[/B][/SIZE] 6x = 14 [SIZE=5][B]Step 5: Divide each side of the equation by 6[/B][/SIZE] 6x/6 = 14/6 x = [B]2.3333333333333[/B]
If f(x) = 3x + 1 and g(x) = x^2 + 2x, find x when f(g(x)) = 10
If f(x) = 3x + 1 and g(x) = x^2 + 2x, find x when f(g(x)) = 10 [U]Evaluate f(g(x))[/U] f(g(x)) = 3(x^2 + 2x) + 1 f(g(x)) = 3x^2 + 6x + 1 [U]When f(g(x)) = 10, we have[/U] 10 = 3x^2 + 6x + 1 [U]Subtract 10 from each side:[/U] 3x^2 + 6x - 9 = 0 Divide each side of the equation by 3 x^2 + 2x - 3 = 0 Factor, we have: (x + 3)(x - 1) = 0 So x is either [B]1 or -3[/B]
if f(x)=-5x+11 and f(n)=21 what does n equal
if f(x)=-5x+11 and f(n)=21 what does n equal f(n) = -5(n) + 11 Since f(n) = 21, we have: -5(n) + 11 = 21 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=-5n%2B11%3D21&pl=Solve']equation solver[/URL], we get [B]n = -2[/B].
If FG = 9, GH = 4x, and FH = 7x, what is GH?
If FG = 9, GH = 4x, and FH = 7x, what is GH? By segment addition, we have: FG + GH = FH Substituting in the values given, we have: 9 + 4x = 7x To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=9%2B4x%3D7x&pl=Solve']type it in our math engine[/URL] and we get: x = 3 The question asks for GH, so with x = 3, we have: GH = 4(3) GH = [B]12[/B]
If FG=11, GH=x-2, and FH=3x-11, what is FH
If FG=11, GH=x-2, and FH=3x-11, what is FH By segment addition, we have: FG + GH = FH 11 + x - 2 = 3x - 11 To solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=11%2Bx-2%3D3x-11&pl=Solve']type it in or math engine[/URL] and we get: x = 10 FH = 3x - 11. So we substitute x = 10 into this: FH = 3(10) - 11 FH = 30 - 11 FH = [B]19[/B]
If Frank�s age is double of Willis� age and the sum of their ages is 42. What are their ages?
If Frank�s age is double of Willis� age and the sum of their ages is 42. What are their ages? Let Frank's age be f. Let Willis's age be w. We're given two equations: [LIST=1] [*]f = 2w <-- Double means multiply by 2 [*]f + w = 42 [/LIST] Substitute equation (1) into equation (2): 2w + w = 42 To solve for w, [URL='https://www.mathcelebrity.com/1unk.php?num=2w%2Bw%3D42&pl=Solve']type this equation into our search engine[/URL]. We get: w = [B]14 [/B] Now, take w = 14, and substitute it back into equation (1) to solve for f: f = 2(14) f = [B]28[/B]
If half the number is added to twice the number, the answer is 50
If half the number is added to twice the number, the answer is 50. Let the number be n. Half is also written as 0.5, and twice is written by multiplying by 2. We have: 0.5n + 2n = 50 [URL='https://www.mathcelebrity.com/1unk.php?num=0.5n%2B2n%3D50&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]n = 20[/B]
If I add 8 to the number and then multiply the result by 6 I get the same answer as when I add 58 to
If I add 8 to the number and then multiply the result by 6 I get the same answer as when I add 58 to a number. Form an equation Let the number be n. We're given: 6(n + 8) = n + 58 Multiply through: 6n + 48 = n + 58 To solve this equation for n, [URL='https://www.mathcelebrity.com/1unk.php?num=6n%2B48%3Dn%2B58&pl=Solve']we type it into our search engine[/URL] and we get: n = [B]2[/B]
If I make 40,000 dollars every 15 minutes then how long will it take me to make a million
If I make 40,000 dollars every 15 minutes then how long will it take me to make a million Let f be the number of fifteen minute blocks. We're given: 40000f = 1000000 To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=40000f%3D1000000&pl=Solve']type this equation into our search engine[/URL] and we get: f = 25 Total minutes = Fifteen minute blocks (f) * 15 minutes Total minutes = 25 * 15 Total minutes = [B]375 minutes or 6 hours and 15 minutes[/B]
If Jody had $3 more she would have twice as much as Lars together they have $60
If Jody had $3 more she would have twice as much as Lars together they have $60. Let j be Jody's money and l be Lars's money. We have two equations: [LIST=1] [*]j + l = 60 [*]j + 3 = 2l [/LIST] Rearrange (2) to solve for j by subtracting 3 j = 2l - 3 Now substitute this into (1) (2l - 3) + l = 60 Combine like terms 3l - 3 = 60 Enter this into our [URL='http://www.mathcelebrity.com/1unk.php?num=3l-3%3D60&pl=Solve']equation calculator[/URL], and we get: [B]l = 21[/B] Now plug l = 21 into our rearranged equation above: j = 2(21) - 3 j = 42 - 3 [B]j = 39[/B]
If Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how m
If Mr hernandez has 5 times as many students as Mr daniels and together they have 150 students how many students do each have? Let h = Mr. Hernandez's students and d = Mr. Daniels students. We are given two equations: (1) h = 5d (2) d + h = 150 Substitute equation (1) into equation (2) d + (5d) = 150 Combine like terms: 6d = 150 Divide each side of the equation by 6 to isolate d d = 25 <-- Mr. Daniels Students Now, plug the value for d into equation (1) h = 5(25) h = 125 <-- Mr. Hernandez students
If p is inversely proportional to the square of q, and p is 2 when q is 4, determine p when q is equ
If p is inversely proportional to the square of q, and p is 2 when q is 4, determine p when q is equal to 2. We set up the variation equation with a constant k such that: p = k/q^2 [I](inversely proportional means we divide) [/I] When q is 4 and p is 2, we have: 2 = k/4^2 2 = k/16 Cross multiply: k = 2 * 16 k = 32 Now, the problem asks for p when q = 2: p = 32/2^2 p = 32/4 p = [B]8[/B]
If p+4=2 and q-3=2, what is the value of qp?
If p+4=2 and q-3=2, what is the value of qp? Isolate p by subtracting 4 from each side using our [URL='http://www.mathcelebrity.com/1unk.php?num=p%2B4%3D2&pl=Solve']equation calculator[/URL] p = -2 Isolate q by adding 3 to each side using our [URL='http://www.mathcelebrity.com/1unk.php?num=q-3%3D2&pl=Solve']equation calculator[/URL]: q = 5 pq = (-2)(5) [B]pq = -10[/B]
If QR = 16, RS = 4x ? 17, and QS = x + 20, what is RS?
If QR = 16, RS = 4x ? 17, and QS = x + 20, what is RS? From the segment addition rule, we have: QR + RS = QS Plugging our values in for each of these segments, we get: 16 + 4x - 17 = x + 20 To solve this equation for x, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2B4x-17%3Dx%2B20&pl=Solve']we type it in our search engine[/URL] and we get: x = 7 Take x = 7 and substitute it into RS: RS = 4x - 17 RS = 4(7) - 17 RS = 28 - 17 RS = [B]11[/B]
If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how ma
If Quinn has 4 times as many quarters as nickels and they have a combined value of 525 cents, how many of each coin does he have? Using q for quarters and n for nickels, and using 525 cents as $5.25, we're given two equations: [LIST=1] [*]q = 4n [*]0.25q + 0.05n = 5.25 [/LIST] Substitute equation (1) into equation (2) for q: 0.25(4n) + 0.05n = 5.25 Multiply through and simplify: n + 0.05n = 5.25 To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B0.05n%3D5.25&pl=Solve']type it in our search engine[/URL] and we get: n = [B]5 [/B] To get q, we plug in n = 5 into equation (1) above: q = 4(5) q = [B]20[/B]
If the equation of a line passes through the points (1, 3) and (0, 0), which form would be used to w
If the equation of a line passes through the points (1, 3) and (0, 0), which form would be used to write the equation of the line? [URL='https://www.mathcelebrity.com/slope.php?xone=1&yone=3&slope=+&xtwo=0&ytwo=0&bvalue=+&pl=You+entered+2+points']Typing (1,3),(0,0) into the search engine[/URL], we get a point-slope form: [B]y - 3 = 3(x - 1)[/B] If we want mx + b form, we have: y - 3 = 3x - 3 Add 3 to each side: [B]y = 3x[/B]
If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide
If the perimeter of a rectangular field is 120 feet and the length of one side is 25 feet, how wide must the field be? The perimeter of a rectangle P, is denoted as: P = 2l + 2w We're given l = 25, and P = 120, so we have 2(25) + 2w = 120 Simplify: 2w + 50 = 120 [URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B50%3D120&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 35[/B]
If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, th
If the perimeter of a rectangular sign is 44cm and the width is 2cm shorter than half the length, then what are the length and width? The perimeter (P) of a rectangle is: 2l + 2w = P We're given P = 44, so we substitute this into the rectangle perimeter equation: 2l + 2w = 44 We're also given w = 0.5l - 2. Substitute the into the Perimeter equation: 2l + 2(0.5l - 2) = 44 Multiply through and simplify: 2l + l - 4 = 44 Combine like terms: 3l - 4 = 44 [URL='https://www.mathcelebrity.com/1unk.php?num=3l-4%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get: [B]l = 16[/B] Substitute this back into the equation w = 0.5l - 2 w = 0.5(16) - 2 w = 8 - 2 [B]w = 6[/B]
if the point (.53,y) is on the unit circle in quadrant 1, what is the value of y?
if the point (.53,y) is on the unit circle in quadrant 1, what is the value of y? Unit circle equation: x^2 + y^2 = 1 Plugging in x = 0.53, we get (0.53)^2 + y^2 = 1 0.2809 + y^2 = 1 Subtract 0.2809 from each side: y^2 = 0.7191 y = [B]0.848[/B]
If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find th
If the speed of an aeroplane is reduced by 40km/hr, it takes 20 minutes more to cover 1200m. Find the time taken by aeroplane to cover 1200m initially. We know from the distance formula (d) using rate (r) and time (t) that: d = rt Regular speed: 1200 = rt Divide each side by t, we get: r = 1200/t Reduced speed. 20 minutes = 60/20 = 1/3 of an hour. So we multiply 1,200 by 3 3600 = (r - 40)(t + 1/3) If we multiply 3 by (t + 1/3), we get: 3t + 1 So we have: 3600 = (r - 40)(3t + 1) Substitute r = 1200/t into the reduced speed equation: 3600 = (1200/t - 40)(3t + 1) Multiply through and we get: 3600 = 3600 - 120t + 1200/t - 40 Subtract 3,600 from each side 3600 - 3600 = 3600 - 3600 - 120t + 1200/t - 40 The 3600's cancel, so we get: - 120t + 1200/t - 40 = 0 Multiply each side by t: -120t^2 - 40t + 1200 = 0 We've got a quadratic equation. To solve for t, [URL='https://www.mathcelebrity.com/quadratic.php?num=-120t%5E2-40t%2B1200%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this in our search engine[/URL] and we get: t = -10/3 or t = 3. Since time [I]cannot[/I] be negative, our final answer is: [B]t = 3[/B]
If thrice a number is increased by 11,the result is 35. What is the number
If thrice a number is increased by 11,the result is 35. What is the number? [LIST] [*]The phrase [I]a number [/I]means an arbitrary variable. Let's call it x. [*]Thrice means multiply by 3, so we have 3x [*]Increased by 11 means we add 11, so we have 3x + 11 [*]The [I]result is[/I] means an equation, so we set 3x + 11 equal to 35 [/LIST] 3x + 11 = 35 <-- This is our algebraic expression The problem ask us to solve the algebraic expression. [URL='https://www.mathcelebrity.com/1unk.php?num=3x%2B11%3D35&pl=Solve']Typing this problem into our search engine[/URL], we get [B]x = 8[/B].
if two angles are supplementary and congruent then they are right angles
if two angles are supplementary and congruent then they are right angles Let the first angle be x. Let the second angle be y. Supplementary angles means their sum is 180: x + y = 180 We're given both angles are congruent, meaning equal. So we set x = y: y + y = 180 To solve for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=y%2By%3D180&pl=Solve']type this equation into our search engine[/URL] and we get: y = [B]90. <-- 90 degrees is a right angle, so this is TRUE[/B]
If x = 2y/3 and y = 18, what is the value of 2x - 3?
If x = 2y/3 and y = 18, what is the value of 2x - 3? A) 21 B) 15 C) 12 D) 10 Substitute the values into the equation: 2(2y/3) - 3 <-- Given x = 2y/3 Simplifying, we have: 4y/3 - 3 Now substitute y = 18 into this: 4(18)/3 - 3 4(6) - 3 24 - 3 [B]21 or Answer A[/B]
if x2 is added to x, the sum is 42
If x2 is added to x, the sum is 42. x^2 + x = 42 Subtract 42 from both sides: x^2 + x - 42 = 0 We have a quadratic equation. Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-42%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation solver[/URL], we get: [B]x = 6 and x = -7 [/B] Since the problem does not state positive number solutions, they are both answers.
If y varies directly as x and inversely as z, then which equation describes the relation?
If y varies directly as x and inversely as z, then which equation describes the relation? Directly means we multiply, inversely means we divide, so we have a constant k such that: [B]y = kx/z[/B]
If y=2x and y=18, what is the value of x
If y=2x and y=18, what is the value of x Since y = 2x [B]and[/B] y = 18, we set 2x equals to 18 since they both equal y 2x = 18 [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D18&pl=Solve']Type this equation into our search engine[/URL] and we get: x = [B]9[/B]
if you add 7 to 2x, the result is 17
if you add 7 to 2x, the result is 17 Add 7 to 2x: 2x + 7 The phrase [I]the result is[/I] means an equation, so we set 2x + 7 = 17 [B]2x + 7 = 17 [/B] <-- This is our algebraic expression Now, if you want to solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B7%3D17&pl=Solve']type in 2x + 7 = 17 into the search engine[/URL], and we get [B]x = 5[/B].
If you have $272, and you spend $17 each day, how long would it be until you had no money left?
If you have $272, and you spend $17 each day, how long would it be until you had no money left? Let d be the number of days. We have a balance expression of: 272 - 17d We want to know when the balance is 0, so we set 272 - 17d equal to 0. 272 - 17d = 0 To solve for d, we [URL='http://272 - 17d = 0']type this equation into our search engine[/URL] and we get: d = [B]16[/B]
If you multiply me by 33 and subtract 20, the result is 46. Who am I?
If you multiply me by 33 and subtract 20, the result is 46. Who am I? [LIST] [*]Start with the variable x [*]Multiply me by 33 = 33x [*]Subtract 20: 33x - 20 [*]The result is 46, means we set this expression equal to 46: 33x - 20 = 46 [/LIST] Run this through our [URL='http://www.mathcelebrity.com/1unk.php?num=33x-20%3D46&pl=Solve']equation calculator[/URL], and we get: [B]x = 2[/B]
If you take a Uber and they charge $5 just to show up and $1.57 per mile, how much will it cost you
If you take a Uber and they charge $5 just to show up and $1.57 per mile, how much will it cost you to go 12 miles? (Assume no tip.) a. Create an equation from the information above. b. Identify the slope in the equation? c. Calculate the total cost of the ride? 2. With the same charges as #1, how many miles could you go with $50, if you also gave a $7.50 tip? (Challenge Question! Hint, you only have a $50, exactly, with you a. Cost Equation C(m) for m miles is as follows: [B]C(m) = 1.57m + 5 [/B] b. Slope of the equation is the coefficient for m, which is [B]1.57 [/B] c. Total cost of the ride for m = 12 miles is: C(12) = 1.57(12) + 5 C(12) = 18.84 + 5 C(12) = [B]23.84 [/B] d. If you give a 7.50 tip, we subtract the tip from the $50 to start with a reduced amount: 50 - 7.50 = 42.50 So C(m) = 42.50 1.57m + 5 = 42.50 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.57m%2B5%3D42.50&pl=Solve']type it in our search engine[/URL] and we get: m = 23.89 Since we deal in full miles, we round our answer down to m = [B]23[/B]
If you triple a number and then add 10, you get one-half of the original number. What is the number
If you triple a number and then add 10, you get one-half of the original number. What is the number? Let the number be n. We have: 3n + 10 = 0.5n Subtract 0.5n from each side 2.5n + 10 = 0 Subtract 10 from each side: 2.5n = -10 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2.5n%3D-10&pl=Solve']equation calculator,[/URL] we get: [B]n = -4[/B]
If you triple me, subract 7, and add 4 you get 42. What number am i?
If you triple me, subract 7, and add 4 you get 42. What number am i? Start with an unknown number, "x". Triple me 3x Subtract 7 3x - 7 Add 4 3x - 7 + 4 You get 42 3x - 7 + 4 = 42 Simplify: 3x - 3 = 42 Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=3x-3%3D42&pl=Solve']equation calculator:[/URL] x = [B]15[/B]
If your parents give you $20 per week and $1.50 per chore, how many chores would you have to do to e
If your parents give you $20 per week and $1.50 per chore, how many chores would you have to do to earn a total of $33.50 that week? Let c be the number of chores. We're given the equation: 1.50c + 20 = 33.50 To solve this equation for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.50c%2B20%3D33.50&pl=Solve']type it in our search engine [/URL]and we get: c = [B]9[/B]
In 16 years, Ben will be 3 times as old as he is right now
In 16 years, Ben will be 3 times as old as he is right now. Let Ben's age today be a. We're given: a + 16 = 3a [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B16%3D3a&pl=Solve']Type this equation into the search engine[/URL], and we get: a = [B]8[/B]
In 20 years charles will be 3 times as old as he is now. How old is he now?
In 20 years charles will be 3 times as old as he is now. How old is he now? Let Charles's age be a today. We're given: a + 20 = 3a [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B20%3D3a&pl=Solve']If we type this equation into our search engine[/URL], we get: [B]a = 10 [/B] Let's check our work in our given equation: 10 + 20 ? 3(10) 30 = 30 <-- Checks out!
In 2000 a company increased its workforce by 50%. In 2001 it decreased its workforce by 50%. How doe
In 2000 a company increased its workforce by 50%. In 2001 it decreased its workforce by 50%. How does the size of its workforce at the end of 2001 compare with the size of the workforce at the beginning of 2000? Let w be the size of the workforce before any changes. We have: [LIST] [*]w(2000) = w(1999) * 1.5 [I](50% increase is the same as multiplying by 1.5)[/I] [*]w(2001) = w(2000)/1.5 [I](50% decrease is the same as dividing by 1.5)[/I] [/LIST] Substitute the first equation back into the second equation w(2001) = w(1999) * 1.5/1.5 Cancel the 1.5 on top and bottom w(2001) = w(1999) This means the workforce had [B]zero net change[/B] from the beginning of 2000 to the end of 2001.
In 56 years, Stella will be 5 times as old as she is right now.
In 56 years, Stella will be 5 times as old as she is right now. Let Stella's age be s. We're given: s + 56 = 5s [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B56%3D5s&pl=Solve']Type this equation into our search engine[/URL], and we get: [B]s = 14[/B]
In 8 years kelly's age will be twice what it is now. How old is kelly?
In 8 years kelly's age will be twice what it is now. How old is kelly? Let Kelly's age be a. In 8 years means we add 8 to a: a + 8 Twice means we multiply a by 2: 2a The phrase [I]will be[/I] means equal to, so we set a + 8 equal to 2a a + 8 = 2a To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=a%2B8%3D2a&pl=Solve']type it in our math engine[/URL] and we get: a = [B]8 [/B] [U]Evaluate a = 8 and check our work[/U] 8 + 8 ? 2(8) 16 = 16 [MEDIA=youtube]y4jaQpkaJEw[/MEDIA]
In a bike shop they sell bicycles & tricycles. I counted 80 wheels & 34 seats. How many bicycles & t
In a bike shop they sell bicycles & tricycles. I counted 80 wheels & 34 seats. How many bicycles & tricycles were in the bike shop? Let b be the number or bicycles and t be the number of tricycles. Since each bicycle has 2 wheels and 1 seat and each tricycle has 3 wheels and 1 seat, we have the following equations: [LIST=1] [*]2b + 3t = 80 [*]b + t = 34 [/LIST] We can solve this set of simultaneous equations 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2b+%2B+3t+%3D+80&term2=b+%2B+t+%3D+34&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2b+%2B+3t+%3D+80&term2=b+%2B+t+%3D+34&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2b+%2B+3t+%3D+80&term2=b+%2B+t+%3D+34&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]b = 22[/B] [*][B]t = 12[/B] [/LIST]
In a certain Algebra 2 class of 26 students, 18 of them play basketball and 7 of them play baseball.
In a certain Algebra 2 class of 26 students, 18 of them play basketball and 7 of them play baseball. There are 5 students who play neither sport. What is the probability that a student chosen randomly from the class plays both basketball and baseball? Students play either basketball only, baseball only, both sports, or no sports. Let the students who play both sports be b. We have: b + 18 + 7 - 5 = 26 <-- [I]We subtract 5 because we don't want to double count the students who played a sport who were counted already [/I] We [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B18%2B7-5%3D26&pl=Solve']type this equation into our search engine[/URL] and get: b = [B]6[/B]
In a class of 30 pupils, 18 take Social Studies and 17 take Technical Drawing, 3 take neither. How m
In a class of 30 pupils, 18 take Social Studies and 17 take Technical Drawing, 3 take neither. How many take both Social Studies and Technical Drawing? Let students who take both be b. We have: 18 + 17 + 3 - b = 30 38 - b = 30 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=38-b%3D30&pl=Solve']equation solver[/URL], we get: b = [B]8[/B]
In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there i
In a class there are 5 more boys than girls. There are 13 students in all. How many boys are there in the class? We start by declaring variables for boys and girls: [LIST] [*]Let b be the number of boys [*]Let g be the number of girls [/LIST] We're given two equations: [LIST=1] [*]b = g + 5 [*]b + g = 13 [/LIST] Substitute equation (1) for b into equation (2): g + 5 + g = 13 Grouping like terms, we get: 2g + 5 = 13 Subtract 5 from each side: 2g + 5 - 5 = 13 - 5 Cancel the 5's on the left side and we get: 2g = 8 Divide each side of the equation by 2 to isolate g: 2g/2 = 8/2 Cancel the 2's on the left side and we get: g = 4 Substitute g = 4 into equation (1) to solve for b: b = 4 + 5 b = [B]9[/B]
In a newspaper, it was reported that yearly robberies in Springfield were up 50% to 351 in 2013 from
In a newspaper, it was reported that yearly robberies in Springfield were up 50% to 351 in 2013 from 2012. How many robberies were there in Springfield in 2012? Let the robberies in 2012 be r. We're given the following equation: 1.5r = 351 <-- We write a 50% increase as 1.5 To solve this equation for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=1.5r%3D351&pl=Solve']type it into our search engine[/URL] and we get: r = [B]234[/B]
In an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two
In an algebra test, the highest grade was 50 points higher than the lowest grade. The sum of the two grades was 180. Let the high grade be h and the low grade be l. We're given: [LIST=1] [*]h = l + 50 [*]h + l = 180 [/LIST] Substitute equation (1) into equation (2) for h l + 50 + l = 180 To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=l%2B50%2Bl%3D180&pl=Solve']we type it in our search engine[/URL] and we get: l = [B]65 [/B] Now, we take l = 65 and substitute it into equation (1) to solve for h: h = 65 + 50 h = [B]115[/B]
In one day, a store sells 14 pairs of jeans. The 14 jeans represent 20% of the total number of items
In one day, a store sells 14 pairs of jeans. The 14 jeans represent 20% of the total number of items sold that day. How many items did the store sell in one day? Explain or show how you got your answer. 14 = 20%s where s is the number of items sold in one day. We can write 20% as 0.2, so we have: 0.2s = 14 [URL='https://www.mathcelebrity.com/1unk.php?num=0.2s%3D14&pl=Solve']Type this equation into the search engine[/URL], and we get: s = [B]70[/B]
In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing
In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? In Super Bowl XXXV, the total number of points scored was 41. The winning team outscored the losing team by 27 points. What was the final score of the game? Let w be the winning team's points, and l be the losing team's points. We have two equations: [LIST=1] [*]w + l = 41 [*]w - l = 27 [/LIST] Add the two equations: 2w = 68 Divide each side by 2 [B]w = 34[/B] Substitute this into (1) 34 + l = 41 Subtract 34 from each side [B]l = 7[/B] Check your work: [LIST=1] [*]34 + 7 = 41 <-- check [*]34 - 7 = 27 <-- check [/LIST] The final score of the game was [B]34 to 7[/B]. You could also use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=w+%2B+l+%3D+41&term2=w+-+l+%3D+27&pl=Cramers+Method']simultaneous equation solver[/URL].
In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the l
In the last year a library bought 237 new books and removed 67 books. There were 5745 books in the library at the end of the year. How many books were in the library at the start of the year Let the starting book count be b. We have: [LIST] [*]We start with b books [*]Buying 237 books means we add (+237) [*]Removing 67 books means we subtract (-67) [*]We end up with 5745 books [/LIST] Our change during the year is found by the equation: b + 237 - 67 = 5745 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B237-67%3D5745&pl=Solve']type this equation into our search engine[/URL] and we get: b = [B]5575[/B]
In this class of 4/5 students are right handed. if there are 20 right handed students, what is the t
In this class of 4/5 students are right handed. if there are 20 right handed students, what is the total number of students in this class? Let x be the total number of students in the class. We have: 4/5x = 20 Cross multiplying or using our [URL='http://www.mathcelebrity.com/1unk.php?num=4x%3D100&pl=Solve']equation calculator[/URL], we get: 4x = 100 Divide each side by 4 [B]x = 25[/B]
Ina has $40 in her bank account and saves $8 a week. Ree has $200 in her bank account and spends $12
Ina has $40 in her bank account and saves $8 a week. Ree has $200 in her bank account and spends $12 a week. Write an equation to represent each girl. Let w equal the number of weeks, and f(w) be the amount of money in the account after w weeks: [LIST] [*]Ina: [B]f(w) = 40 + 8w[/B] [LIST] [*]We add because Ina saves money, so her account grows [/LIST] [*]Ree: [B]f(w) = 200 - 12w[/B] [LIST] [*]We subtract because Ree saves [/LIST] [/LIST]
Income and Price Elasticity
Solves for any one of the 5 components that make up the income/price elasticity of demand equation.
Is (3,10) a solution to the equation y=4x
Is (3,10) a solution to the equation y=4x Plug in the numbers to check: 10 ? 4(3) 10 <> 12 No, this is [B]not a solution[/B]
Is (9, 6) a solution to the equation y = x - 3?
Is (9, 6) a solution to the equation y = x - 3? The ordered pair (x, y) = (9, 6) Plug in x = 9 into y = x - 3: y = 9 - 3 y = 6 [B]Yes, (9, 6) is a solution to the equation y = x - 3[/B]
Is 30 a solution to 2x + 5 = 3x - 25
Is 30 a solution to 2x + 5 = 3x - 25 Let's test x = 30 into our equation: 2(30) + 5 ? 3(30) - 25 60 + 5 ? 90 - 25 65 = 65 [B]Yes, x = 30 is a solution[/B]. If you wanted to solve for x with simplification, you can [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D3x-25&pl=Solve']type it in our search engine[/URL] and get: x = 30
is parallel to the x-axis and has an y-intercept of 3
is parallel to the x-axis and has an y-intercept of 3 Parallel to the x axis means it runs through the y-axis y-intercept of 3 means our equation is [B]y = 3[/B]
Is the point (4,7) a solution of the equation yequals15xminus8?
Is the point (4,7) a solution of the equation y equals 15x minus 8? Plug in x = 4: 15(4) - 8 60 - 8 52 Since 52 <> 4, (4,7) is [U][B]not[/B][/U] a solution of the equation y equals 15x minus 8
Is this algebra?
Can anyone answer this equation? You start off with 5 tickets and every 24min you get 1 extra ticket. After you sell your first ticket you have exactly 10min to sell another ticket and so on. How many tickets can you sell before you run out of tickets to sell? Plz give the mathematical equation for others to know also[IMG]https://www.facebook.com/images/emoji.php/v9/f34/1/16/1f914.png[/IMG]
Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. Ho
Isabel is making face mask. She spends $50 on supplies and plans on selling them for $4 per mask. How many mask does have to make in order to make a profit equal to $90? [U]Set up the cost function C(m) where m is the number of masks:[/U] C(m) = supply cost C(m) = 50 [U]Set up the cost function R(m) where m is the number of masks:[/U] R(m) = Sale Price * m R(m) = 4m [U]Set up the profit function P(m) where m is the number of masks:[/U] P(m) = R(m) - C(m) P(m) = 4m - 50 The problems asks for profit of 90, so we set P(m) = 90: 4m - 50 = 90 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=4m-50%3D90&pl=Solve']type it in our search engine[/URL] and we get: m = [B]35[/B]
Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only
[SIZE=4]Ishaan is 72 years old and William is 4 years old. How many years will it take until Ishaan is only 5 times as old as William? [U]Express Ishaan and William's age since today where y is the number of years since today, we have:[/U] i = 72+y w = 4+y [U]We want the time for Ishaan age will be 5 times William's age:[/U] i = 5w 72 + y = 5(4 + y) We [URL='https://www.mathcelebrity.com/1unk.php?num=72%2By%3D5%284%2By%29&pl=Solve']plug this equation into our search engine [/URL]and get: y = [B]13[/B] [/SIZE]
It costs $2.50 to rent bowling shoes. Each game costs $2.25. You have $9.25. How many games can you
It costs $2.50 to rent bowling shoes. Each game costs $2.25. You have $9.25. How many games can you bowl. Writing an equation and give your answer. Let the number of games be g. we have the function C(g): C(g) = cost per game * g + bowling shoe rental C(g) = 2.25g + 2.50 The problem asks for g when C(g) = 9.25 2.25g + 2.50 = 9.25 To solve this equation, we[URL='https://www.mathcelebrity.com/1unk.php?num=2.25g%2B2.50%3D9.25&pl=Solve'] type it in our search engine[/URL] and we get: g = [B]3[/B]
It takes 60 minutes for 7 people to paint 5 walls. How many minutes does it take 10 people to paint
It takes 60 minutes for 7 people to paint 5 walls. How many minutes does it take 10 people to paint 10 walls? Rate * Time = Output Let "Rate" (r) be the rate at which [B]one person[/B] works. So we have: 7r * 60 = 5 Multiply through and simplify: 420r = 5 Divide each side by 5 to isolate r: r = 1/84 So now we want to find out how many minutes it takes 10 people to paint 10 walls using this rate: 10rt = 10 With r = 1/84, we have: 10t/84 = 10 Cross multiply: 10t = 840 To solve for t, we t[URL='https://www.mathcelebrity.com/1unk.php?num=10t%3D840&pl=Solve']ype this equation into our search engine[/URL] and we get: t = [B]84 minutes[/B]
Jack bought 7 tickets for a movie. He paid $7 for each adult ticket and $4 for each child ticket. Ja
Jack bought 7 tickets for a movie. He paid $7 for each adult ticket and $4 for each child ticket. Jack spent $40 for the tickets Let a = Number of adult tickets and c be the number of child tickets. [LIST=1] [*]7a + 4c = 40 [*]a + c = 7 [*]Rearrange (2): a = 7 - c [/LIST] Now substitute a in (3) into (1): 7(7 - c) + 4c = 40 49 - 7c + 4c = 40 49 - 3c = 40 Add 3c to each side and subtract 40: 3c = 9 Divide each side by 3: [B]c = 3 [/B] Substitute c = 3 into Equation (2) a + 3 = 7 Subtract 3 from each side: [B]a = 4[/B]
Jack bought a car for $17,500. The car loses $750 in value each year. Which equation represents the
Jack bought a car for $17,500. The car loses $750 in value each year. Which equation represents the situation? Let y be the number of years since Jack bought the car. We have a Book value B(y): [B]B(y) = 17500 - 750y[/B]
Jack has 34 bills and coins in 5�s and 2�s. The total value is $116. How many 5 dollar bills does he
Jack has 34 bills and coins in 5�s and 2�s. The total value is $116. How many 5 dollar bills does he have? Let the number of 5 dollar bills be f. Let the number of 2 dollar bills be t. We're given two equations: [LIST=1] [*]f + t = 34 [*]5f + 2t = 116 [/LIST] We have a system of equations, which we can solve 3 ways: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=f+%2B+t+%3D+34&term2=5f+%2B+2t+%3D+116&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answers: [LIST] [*][B]f = 16[/B] [*][B]t = 18[/B] [/LIST]
Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocola
Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left. If Jack had 2 chocolates left, then the total given to his friends is: 50 - 2 = 48 Let f be the number of friends at his birthday party. Then we have: 3f = 48 [URL='https://www.mathcelebrity.com/1unk.php?num=3f%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]f = 16[/B]
Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocola
Jack's mother gave him 50 chocolates to give to his friends at his birthday party. He gave 3 chocolates to each of his friends and still had 2 chocolates left. Let f be the number of Jacks's friends. We have the following equation to represent the chocolates: 3f + 2 = 50 To solve this equation for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=3f%2B2%3D50&pl=Solve']type it in the math engine[/URL] and we get: f = [B]16[/B]
Jada scored 15 points in one basketball game and p points in another. Her two-game total is 34 point
Jada scored 15 points in one basketball game and p points in another. Her two-game total is 34 points The phrase [I]total[/I] means a sum, so we have the following equation: 15 + p = 34 To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=15%2Bp%3D34&pl=Solve']type this equation into our search engine [/URL]and we get: p = [B]19[/B]
Jake bought s shirts. they were $7 each. Write an equation to represent the total amount that Jake p
Jake bought s shirts. they were $7 each. Write an equation to represent the total amount that Jake paid for the shirts Since Amount = Price * Quantity, we have: [B]7s[/B]
Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episod
Jake Callahan stars in the new TV series Stone Simons: Kid Astronaut. The day after the first episode airs, Jake receives a bunch of fan mail. He splits all the letters into 3 equal stacks to open with his mom and his sister. Each stack contains 21 letters. Which equation can you use to find the number of letters n Jake receives? The number of letters n is represented by number of stacks (s) times letter per stack (l). We're given s = 3 and l = 21, so we have: n = 21(3) n = [B]63[/B]
Jake used 5 boxes to pack 43.5 kg of books. If the boxes each weighed the same and held 8 books, wh
Jake used 5 boxes to pack 43.5 kg of books. If the boxes each weighed the same and held 8 books, what did each book weigh? [U]Set up equations were w is the weight of each book:[/U] [LIST=1] [*]5 boxes * 8 books * w = 43.5 [*]40w = 43.5 [/LIST] [U]Divide each side by 40[/U] [B]w = 1.0875 kg[/B]
James is four time as old as peter if their combined age is 30 how old is James.
James is four time as old as peter if their combined age is 30 how old is James. Let j be Jame's age. Let p be Peter's age. We're given: [LIST=1] [*]j = 4p [*]j + p = 30 [/LIST] Substitute (1) into (2) 4p + p = 30 Combine like terms: 5p = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=5p%3D30&pl=Solve']Type 5p = 30 into our search engine[/URL], and we get p = 6. Plug p = 6 into equation (1) to get James's age, we get: j = 4(6) j = [B]24[/B]
Jane did this calculation a. Add -12 b.subtract -9 c. Add 8 d. Subtract -2 the result is -5. What wa
Jane did this calculation a. Add -12 b.subtract -9 c. Add 8 d. Subtract -2 the result is -5. What was the original number? Let the original number be n. [LIST=1] [*]Add -12: n - 12 [*]Subtract -9: n - 12 - -9 = n - 12 + 9 [*]Add 8: n - 12 + 9 + 8 [*]Subtract - 2: n - 12 + 9 + 8 - -2 = n - 12 + 9 + 8 + 2 [*]The result is -5. So we build the following equation: [/LIST] n - 12 + 9 + 8 + 2 = -5 To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n-12%2B9%2B8%2B2%3D-5&pl=Solve']type it in our search engine[/URL] and we get: [B]n = -12[/B]
Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling?
Janet drove 395 kilometers and the trip took 5 hours. How fast was Janet traveling? Distance = Rate * Time We're given D = 395 and t = 5 We want Rate. We divide each side of the equation by time: Distance / Time = Rate * Time / Time Cancel the Time's on each side and we get: Rate = Distance / Time Plugging our numbers in, we get: Rate = 395/5 Rate = [B]79 kilometers[/B]
Jay purchased tickets for a concert. To place the order, a handling charge of $7 per ticket was cha
Jay purchased tickets for a concert. To place the order, a handling charge of $7 per ticket was charged. A sales tax of 4% was also charged on the ticket price and the handling charges. If the total charge for four tickets was $407.68, what was the ticket price? Round to the nearest dollar. with a ticket price of t, we have the total cost written as: 1.04 * (7*4 + 4t)= 407.68 Divide each side by 1.04 1.04 * (7*4 + 4t)/1.04= 407.68/1.04 Cancel the 1.04 on the left side and we get: 7*4 + 4t = 392 28 + 4t = 392 To solve this equation for t, we [URL='https://www.mathcelebrity.com/1unk.php?num=28%2B4t%3D392&pl=Solve']type it in our math engine[/URL] and we get: t = [B]91[/B]
Jennifer added $120 to her savings account during July. If this brought her balance to $700, how muc
Jennifer added $120 to her savings account during July. If this brought her balance to $700, how much has she saved previously? We have a starting balance s. We're given: s + 120 = 700 To solve this equation for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B120%3D700&pl=Solve']type it in our search engine[/URL] and we get: s = [B]580[/B]
Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age
Jennifer is twice as old as Peter. The difference between their ages is 15. What is Peters age Let j be Jennifer's age Let p be Peter's age We're given two equations: [LIST=1] [*]j = 2p [*]j - p = 15 [/LIST] Substitute equation (1) into equation (2) for j 2p - p = 15 To solve for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=2p-p%3D15&pl=Solve']type this equation into our calculation engine[/URL] and we get: p = [B]15[/B]
Jennifer spent $11.25 on ingredients for cookies shes making for the school bake sale. How many cook
Jennifer spent $11.25 on ingredients for cookies shes making for the school bake sale. How many cookies must she sale at $0.35 apiece to make profit? Let x be the number of cookies she makes. To break even, she must sell: 0.35x = 11.25 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=0.35x%3D11.25&pl=Solve']equation calculator[/URL], and we get: x = 32.14 This means she must sell [B]33[/B] cookies to make a profit.
Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did
Jenny added $150 to her savings account in July. At the end if the month she had $500. How much did she start with? Let the starting balance be s. A deposit means we added 150 to s to get 500. We set up this equation below: s + 150 = 500 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B150%3D500&pl=Solve']type this equation into our search engine[/URL] and we get: s = 3[B]50[/B]
Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many
Jenny has $1200 and is spending $40 per week. Kelsey has $120 and is saving $50 a week. In how many weeks will Jenny and Kelsey have the same amount of money? Jenny: Let w be the number of weeks. Spending means we subtract, so we set up a balance equation B(w): B(w) = 1200 - 40w Kelsey: Let w be the number of weeks. Saving means we add, so we set up a balance equation B(w): B(w) = 120 + 50w When they have the same amount of money, we set the balance equations equal to each other: 1200 - 40w = 120 + 50w To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-40w%3D120%2B50w&pl=Solve']type this equation into our search engine[/URL] and we get: w = [B]12[/B]
Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after wo
Jenny makes 9 dollars for each hour of work. Write an equation to represent her total pay p after working h hours. Since Jenny makes 9 dollars for each hour of work, then her total pay (p) is her hourly rate times the number of hours worked: [B]p = 9h[/B]
Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined
Jenny threw the javelin 4 metres further than Angus but 5 metres less than Cameron. if the combined distance thrown by the 3 friends is 124 metres, how far did Angus throw the javelin? Assumptions and givens: [LIST] [*]Let a be the distance Angus threw the javelin [*]Let c be the distance Cameron threw the javelin [*]Let j be the distance Jenny threw the javelin [/LIST] We're given 3 equations: [LIST=1] [*]j = a + 4 [*]j = c - 5 [*]a + c + j = 124 [/LIST] Since j is the common variable in all 3 equations, let's rearrange equation (1) and equation (2) in terms of j as the dependent variable: [LIST=1] [*]a = j - 4 [*]c = j + 5 [*]a + c + j = 124 [/LIST] Now substitute equation (1) and equation (2) into equation (3) for a and c: j - 4 + j + 5 + j = 124 To solve this equation for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=j-4%2Bj%2B5%2Bj%3D124&pl=Solve']type it in our math engine[/URL] and we get: j = 41 The question asks how far Angus (a) threw the javelin. Since we have Jenny's distance j = 41 and equation (1) has j and a together, let's substitute j = 41 into equation (1): a = 41 - 4 a = [B]37 meters[/B]
Jenny went shoe shopping. Now she has 5 more pairs than her brother. Together they have 25 pairs. Ho
Jenny went shoe shopping. Now she has 5 more pairs than her brother. Together they have 25 pairs. How many pairs does Jenny have and how many pairs does her brother have? [U]Let j be the number of shoes Jenny has and b be the number of s hoes her brother has. Set up 2 equations:[/U] (1) b + j = 25 (2) j = b + 5 [U]Substitute (2) into (1)[/U] b + (b + 5) = 25 [U]Group the b terms[/U] 2b + 5 = 25 [U]Subtract 5 from each side[/U] 2b = 20 [U]Divide each side by b[/U] [B]b = 10 [/B] [U]Substitute b = 10 into (2)[/U] j = 10 + 5 [B]j = 15[/B]
Jessica tutors chemistry. For each hour that she tutors, she earns 30 dollars. Let E be her earnings
Jessica tutors chemistry. For each hour that she tutors, she earns 30 dollars. Let E be her earnings (in dollars) after tutoring for H hours. Write an equation relating E to H . Then use this equation to find Jessicas earnings after tutoring for 19 hours. Set up a function of h hours for tutoring: [B]E(h) = 30h[/B] We need to find E(19) E(19) = 30(19) E(19) = [B]570[/B]
Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes f
Jill and Jack are getting vegetables from the Farmer's Market. Jill buys 12 carrots and 8 tomatoes for $34. Jack buys 10 carrots and 7 tomatoes for $29. How much does each carrot and each tomato cost? Let the cost of carrots be c and the cost of tomatoes be t. Since the total cost is price times quantity, We're given two equations: [LIST=1] [*]12c + 8t = 34 <-- Jill [*]10c + 7t = 29 <-- Jack [/LIST] We have a system of equations. We can solve this one of three ways: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12c+%2B+8t+%3D+34&term2=10c+%2B+7t+%3D+29&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [LIST] [*][B]t = 2[/B] [*][B]c = 1.5[/B] [/LIST]
Jim has $440 in his savings account and adds $12 per week to the account. At the same time, Rhonda h
Jim has $440 in his savings account and adds $12 per week to the account. At the same time, Rhonda has $260 in her savings account and adds $18 per week to the account. How long will it take Rhonda to have the same amount in her account as Jim? [U]Set up Jim's savings function S(w) where w is the number of weeks of savings:[/U] S(w) = Savings per week * w + Initial Savings S(w) = 12w + 440 [U]Set up Rhonda's savings function S(w) where w is the number of weeks of savings:[/U] S(w) = Savings per week * w + Initial Savings S(w) = 18w + 260 The problems asks for w where both savings functions equal each other: 12w + 440 = 18w + 260 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12w%2B440%3D18w%2B260&pl=Solve']type this equation into our math engine[/URL] and we get: w = [B]30[/B]
Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82,
Jim is 9 years older than June. Alex is 8 years younger than June. If the total of their ages is 82, how old is the eldest of them Let j be Jim's age, a be Alex's age, and u be June's age. We have 3 given equations: [LIST=1] [*]j + a + u = 82 [*]j = u + 9 [*]a = u - 8 [/LIST] Substitute (2) and (3) into (1) (u + 9) + (u - 8) + u = 82 Combine Like Terms: 3u + 1 = 82 [URL='https://www.mathcelebrity.com/1unk.php?num=3u%2B1%3D82&pl=Solve']Type this equation into the search engine[/URL], and we get u = 27. The eldest (oldest) of the 3 is Jim. So we have from equation (2) j = u + 9 j = 27 + 9 [B]j = 36[/B]
Jim works for his dad and earns $400 every week plus $22 for every chair (c) he sells. Write an equa
Jim works for his dad and earns $400 every week plus $22 for every chair (c) he sells. Write an equation that can be used to determine jims weekly salary (S) given the number of chairs (c) he sells. [B]S(c) = 400 + 22c[/B]
Jimmy was given $16 for washing the dog.He now has $47. How much money did he start with?
Jimmy was given $16 for washing the dog. He now has $47. How much money did he start with? Let his starting money be s. We're told: s + 16 = 47 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B16%3D47&pl=Solve']type this equation into our search engin[/URL]e and we get: s = [B]31[/B]
Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $18.25 to bu
Jody is buying a scrapbook and sheets of designer paper. She has $40 and needs at least $18.25 to buy the scrapbook. Each sheet of paper costs $0.34. How many sheets of paper can she buy? Set up a cost equation for the number of pieces of paper (p): 0.34p + 18.25 <= 40 <-- we have an inequality since we can't go over 40 [URL='https://www.mathcelebrity.com/1unk.php?num=0.34p%2B18.25%3C%3D40&pl=Solve']Type this inequality into our search engine[/URL] and we get: p <= 63.97 We round down, so we get p = [B]63[/B].
Joe buys 9 cds for the same price, he also buys a dvd for 20. His total bill is 119. Find the cost o
Joe buys 9 cds for the same price, he also buys a dvd for 20. His total bill is 119. Find the cost of one cd. [U]Let c be the cost of one CD. Set up the equation:[/U] 9c + 20 = 119 [U]Use the [URL='http://www.mathcelebrity.com/1unk.php?num=9c%2B20%3D119&pl=Solve']equation solver[/URL]:[/U] [B]c = 11[/B]
Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different accou
Joe opens a bank account that starts with $20 and deposits $10 each week. Bria has a different account that starts with $1000 but withdraws $15 each week. When will Joe and Bria have the same amount of money? Let w be the number of weeks. Deposits mean we add money and withdrawals mean we subtract money. [U]Joe's Balance function B(w) where w is the number of weeks:[/U] 20 + 10w [U]Bria's Balance function B(w) where w is the number of weeks:[/U] 1000 - 15w [U]The problem asks for when both balances will be the same. So we set them equal to each other and solve for w:[/U] 20 + 10w = 1000 - 15w To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=20%2B10w%3D1000-15w&pl=Solve']type this equation into our search engine[/URL] and we get: w = 39.2 We round up to full week and get: w = [B]40[/B]
joe plans to watch 3 movies each month. white an equation to represent the total number of movies n
joe plans to watch 3 movies each month. white an equation to represent the total number of movies n that he will watch in m months Build movie equation. 3 movies per month at m months means we multiply: [B]n = 3m[/B]
Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales.
Joe worked in a shoe department where he earned $325 weekly and 6.5% commission on all of his sales. What was joe�s total sales if he earned $507 last week Let s be total Sales. 6.5% is 0.065 as a decimal, so Joe's earnings are given by: 0.065s + 325 = 507 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.065s%2B325%3D507&pl=Solve']type this equation into our math engine[/URL] and we get: s = [B]2800[/B]
Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which
Joel bought 88 books. Some books cost $13 each and some cost $17 each. In all, he spent $128. Which system of linear equations represents the given situation? Let a be the number of the $13 book, and b equal the number of $17 books. We have the following system of linear equations: [LIST=1] [*][B]a + b = 88[/B] [*][B]13a + 17b = 128[/B] [/LIST] To solve this system, use our calculator for the following methods: [LIST] [*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Substitution']Substitution[/URL] [*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Elimination']Elimination[/URL] [*][URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+b+%3D+88&term2=13a+%2B+17b+%3D+128&pl=Cramers+Method']Cramers Method[/URL] [/LIST]
John earns $5 mowing lawns. How many hours must he work to earn $40?
John earns $5 mowing lawns. How many hours must he work to earn $40? Let hours worked be h. We have: Earnings = Hourly Rate * Hours Worked 40 = 5h To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=40%3D5h&pl=Solve']type it in our search engine[/URL] and we get: h = [B]8[/B]
John read the first 114 pages of a novel, which was 3 pages less than 1/3
John read the first 114 pages of a novel, which was 3 pages less than 1/3 Set up the equation for the number of pages (p) in the novel 1/3p - 3 = 114 Add 3 to each side 1/3p = 117 Multiply each side by 3 [B]p = 351[/B]
John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel.
John read the first 114 pages of a novel, which was 3 pages less than 1/3 of the novel. Let n be the number of pages in the novel. We have: 1/3n - 3 = 114 Multiply each side by 3: n - 9 = 342 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=n-9%3D342&pl=Solve']equation solver[/URL], we get [B]n = 351[/B].
John spent $10.40 on 5 notebooks and 5 pens. Ariana spent $7.00 on 4 notebooks and 2 pens. What is t
John spent $10.40 on 5 notebooks and 5 pens. Ariana spent $7.00 on 4 notebooks and 2 pens. What is the ost of 1 notebook and what is the cost of 1 pen? Let the number of notebooks be n and the number of pens be p. We have two equations: [LIST=1] [*]5n + 5p = 10.40 [*]4n + 2p = 7 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=5n+%2B+5p+%3D+10.40&term2=4n+%2B+2p+%3D+7&pl=Cramers+Method']simultaneous equation calculator[/URL], we have: [LIST] [*][B]n = 1.42[/B] [*][B]p = 0.66[/B] [/LIST]
John took 20,000 out of his retirement and reinvested it. He earned 4% for one investment and 5% on
John took 20,000 out of his retirement and reinvested it. He earned 4% for one investment and 5% on the other. How much did he invest in each if the total amount earned was 880? The first principal portion is x. Which means the second principal portion is 20,000 - x. We have: 0.04x + 0.05(20,000 - x) = 880 0.04x + 1,000 - 0.05x = 880 Group like terms: -0.01x + 1000 = 880 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=-0.01x%2B1000%3D880&pl=Solve']equation solver[/URL], we get x = [B]12,000[/B]. Which means the other fund has 20,000 - 12,000 = [B]8,000[/B].
Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he ru
Johnny Rocket can run 300 meters in 90 seconds. If his speed remains constant, how far could he run in 500 seconds? Round to one decimal place. Set up the distance equation: Distance = Rate * Time 300 = 90r Solving this equation for r, we [URL='https://www.mathcelebrity.com/1unk.php?num=300%3D90r&pl=Solve']type it in our search engine[/URL] and we get: r = 3.333 For 500 seconds, we set up our distance equation again: Distance = 500 * 3.333333 Distance = [B]1666.7 meters[/B]
Joint Variation Equations
Given a joint variation (jointly proportional) of a variable between two other variables with a predefined set of conditions, this will create the joint variation equation and solve based on conditions.
Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15%
Jonathan earns a base salary of $1500 plus 10% of his sales each month. Raymond earns $1200 plus 15% of his sales each month. How much will Jonathan and Raymond have to sell in order to earn the same amount each month? [U]Step 1: Set up Jonathan's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 10% written as a decimal is 0.1. We want decimals to solve equations easier. S(m) = 0.1m + 1500 [U]Step 2: Set up Raymond's sales equation S(m) where m is the amount of sales made each month:[/U] S(m) = Commission percentage * m + Base Salary 15% written as a decimal is 0.15. We want decimals to solve equations easier. S(m) = 0.15m + 1200 [U]The question asks what is m when both S(m)'s equal each other[/U]: The phrase [I]earn the same amount [/I]means we set Jonathan's and Raymond's sales equations equal to each other 0.1m + 1500 = 0.15m + 1200 We want to isolate m terms on one side of the equation. Subtract 1200 from each side: 0.1m + 1500 - 1200 = 0.15m + 1200 - 1200 Cancel the 1200's on the right side and we get: 0.1m - 300 = 0.15m Next, we subtract 0.1m from each side of the equation to isolate m 0.1m - 0.1m + 300 = 0.15m - 0.1m Cancel the 0.1m terms on the left side and we get: 300 = 0.05m Flip the statement since it's an equal sign to get the variable on the left side: 0.05m = 300 To solve for m, we divide each side of the equation by 0.05: 0.05m/0.05 = 300/0.05 Cancelling the 0.05 on the left side, we get: m = [B]6000[/B]
Jose has scored 556 points on his math tests so far this semester. To get an A for the semester, he
Jose has scored 556 points on his math tests so far this semester. To get an A for the semester, he must score at least 660 points. Write and solve an inequality to find the minimum number of points he must score on the remaining tests, n, in order to get an A. We want to know n, such that 556 + n >= 660. <-- We use >= symbol since at least means greater than or equal to. 556 + n >= 660 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=556%2Bn%3E%3D660&pl=Solve']equation/inequality calculator[/URL], we get [B]n >= 104[/B]
Jow buys 9 CD�s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. W
Jow buys 9 CD�s for the same price, and also a cassette tape for $9.45. His total bill was 118.89. What was the cost of one CD? Let the price of each cd be c. We're given the equation: 9c + 9.45 = 118.89 [URL='https://www.mathcelebrity.com/1unk.php?num=9c%2B9.45%3D118.89&pl=Solve']We type this equation into our search engine[/URL] and we get: c = [B]12.16[/B]
Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. Wh
Justin is older than Martina. The difference in their ages is 22 and the sum of their ages is 54. What age is Martina? [U]Assumptions and givens:[/U] [LIST] [*]Let Justin's age be j [*]Let Martina's age be m [*]j > m ([I]since Justin is older than Martina[/I]) [/LIST] We're given the following equations : [LIST=1] [*]j - m = 22 [*]j + m = 54 [/LIST] Since the coefficients of m are opposites, we can take a shortcut using the [I]elimination method[/I] and add equation (1) to equation (2) (j + j) + (m - m) = 22 + 54 2j = 76 To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=2j%3D76&pl=Solve']type this equation into our math engine[/URL] and we get: j = 38 The question asks for Martina's age (m), so we can pick equation (1) or equation (2). Let's use equation (1): 38 - m = 22 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=38-m%3D22&pl=Solve']type it in our math engine[/URL] and we get: m = [B]16[/B]
Kaitlin is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the nu
Kaitlin is a software saleswoman. Let y represent her total pay (in dollars). Let x represent the number of copies of Math is Fun she sells. Suppose that x and y are related by the equation 2500+110x=y. What is Kaitlin totalm pay if she doesnt sell any copies of Math is Fun? We want the value of y when x = 0. y = 2500 + 110(o) y = 2500 + 0 [B]y = 2500[/B]
Karen earns $20 per hour and already has $400 saved, and wants to save $1200. How many hours until b
Karen earns $20 per hour and already has $400 saved, and wants to save $1200. How many hours until bob gets his $1200 goal? Set up he savings function S(h) where h is the number of hours needed: S(h) = savings per hour * h + current savings amount S(h) = 20h + 400 The question asks for h when S(h) = 1200: 20h + 400 = 1200 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=20h%2B400%3D1200&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]40[/B]
Karmen just got hired to work at Walmart. She spent $15 on her new uniform and she gets paid $8 per
Karmen just got hired to work at Walmart. She spent $15 on her new uniform and she gets paid $8 per hour. Write an equation that represents how much money she profits after working for a certain number of hours. How many hours will she have to work for in order to buy a new snowboard ( which costs $450) Her profit equation P(h) where h is the number of hours worked is: [B]P(h) = 8h - 15[/B] Note: [I]We subtract 15 as the cost of Karmen's uniform. [/I] Next, we want to see how many hours Karmen must work to buy a new snowboard which costs $450. We set the profit equation equal to $450 8h - 15 = 450 [URL='https://www.mathcelebrity.com/1unk.php?num=8h-15%3D450&pl=Solve']Typing 8h - 15 = 450 into the search engine[/URL], we get h = 58.13. We round this up to 59 hours.
kate is twice as old as her sister mars. the sum of their ages is 24. find their ages.
kate is twice as old as her sister mars. the sum of their ages is 24. find their ages. Let k be Kate's age Let m be Mars's age We're given two equations: [LIST=1] [*]k = 2m. (Because twice means multiply by 2) [*]k + m = 24 [/LIST] Substitute equation (1) for k into equation (2): 2m + m = 24 T o solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=2m%2Bm%3D24&pl=Solve']type this equation into our math engine[/URL]: m = [B]8 [/B] We want to solve for k using m= 8. Substitute this into equation 1 k = 2(8) k = [B]16 [/B] Check our work for equation 1 16 = 2 * 8 16 = 16 Check our work for equation 2 16 + 8 ? 24 24 = 24 [MEDIA=youtube]TJMTRYP-Ct8[/MEDIA]
Kate spent 1 more than Lauren, and together they spent 5
Kate spent 1 more than Lauren, and together they spent 5. Let k be the amount Kate spent, and l be the amount Lauren spent. We're given: [LIST=1] [*]k = l + 1 [*]k + l = 5 [/LIST] Substitute (1) into (2): (l + 1) + l = 5 Group like terms 2l + 1 = 5 [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B1%3D5&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]l = 2[/B] Plug this into Equation (1), we get: k = 2 + 1 [B]k = 3 [/B] Kate Spent 3, and Lauren spent 2
Katie is twice as old as her sister Mara. The sum of their age is 24.
Let k = Katie's age and m = Mara's age. We have 2 equations: (1) k = 2m (2) k + m = 24 Substitute (1) into (2) (2m) + m = 24 Combine like terms: 3m = 24 Divide each side of the equation by 3 to isolate m m = 8 If m = 8, substituting into (1) or (2), we get k = 16.
Kayla has $1500 in her bank account. She spends $150 each week. Write an equation in slope-intercept
Kayla has $1500 in her bank account. She spends $150 each week. Write an equation in slope-intercept form that represents the relationship between the amount in Kayla's bank account, A, and the number of weeks she has been spending, w [LIST] [*]Slope intercept form is written as A = mw + b [*]m = -150, since spending is a decrease [*]b = 1500, since this is what Kayla starts with when w = 0 [/LIST] [B]A = -150w + 1500[/B]
Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 a
Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 at the end of the summer. He withdraws $25 per week for food, clothing, and movie tickets. How many weeks can Keith withdraw money from his account Our account balance is: 500 - 25w where w is the number of weeks. We want to know the following for w: 500 - 25w = 200 [URL='https://www.mathcelebrity.com/1unk.php?num=500-25w%3D200&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 12[/B]
Kellie has only $5.25 to buy breakfast. She wants to buy as many carrot muffins as she can. Each muf
Kellie has only $5.25 to buy breakfast. She wants to buy as many carrot muffins as she can. Each muffin costs $0.75. What�s an equation? Let m be the number of muffins. Cost equals price * quantity, so we have: [B]0.75m = 5.25 [/B] To solve the equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.75m%3D5.25&pl=Solve']type the equation into our search engine[/URL] and we get: m = [B]7[/B]
Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of sla
Kelly took clothes to the cleaners 3 times last month. First, she brought 4 shirts and 1 pair of slacks and paid11.45. Then she brought 5 shirts, 3 pairs of slacks, and 1 sports coat and paid 27.41. Finally, she brought 5 shirts and 1 sports coat and paid 16.94. How much was she charged for each shirt, each pair of slacks, and each sports coat? Let s be the cost of shirts, p be the cost of slacks, and c be the cost of sports coats. We're given: [LIST=1] [*]4s + p = 11.45 [*]5s + 3p + c = 27.41 [*]5s + c = 16.94 [/LIST] Rearrange (1) by subtracting 4s from each side: p = 11.45 - 4s Rearrange (3)by subtracting 5s from each side: c = 16.94 - 5s Take those rearranged equations, and plug them into (2): 5s + 3(11.45 - 4s) + (16.94 - 5s) = 27.41 Multiply through: 5s + 34.35 - 12s + 16.94 - 5s = 27.41 [URL='https://www.mathcelebrity.com/1unk.php?num=5s%2B34.35-12s%2B16.94-5s%3D27.41&pl=Solve']Group like terms using our equation calculator [/URL]and we get: [B]s = 1.99 [/B] <-- Shirt Cost Plug s = 1.99 into modified equation (1): p = 11.45 - 4(1.99) p = 11.45 - 7.96 [B]p = 3.49[/B] <-- Slacks Cost Plug s = 1.99 into modified equation (3): c = 16.94 - 5(1.99) c = 16.94 - 9.95 [B]c = 6.99[/B] <-- Sports Coat cost
Kendra has $5.70 in quarters and nickels. If she has 12 more quarters than nickels, how many of each
Kendra has $5.70 in quarters and nickels. If she has 12 more quarters than nickels, how many of each coin does she have? Let n be the number of nickels and q be the number of quarters. We have: [LIST=1] [*]q = n + 12 [*]0.05n + 0.25q = 5.70 [/LIST] Substitute (1) into (2) 0.05n + 0.25(n + 12) = 5.70 0.05n + 0.25n + 3 = 5.70 Combine like terms: 0.3n + 3 = 5.70 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.3n%2B3%3D5.70&pl=Solve']equation calculator[/URL], we get [B]n = 9[/B]. Substituting that back into (1), we get: q = 9 + 12 [B]q = 21[/B]
Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How
Kendra is half as old as Morgan and 3 years younger than Lizzie. The total of their ages is 39. How old are they? Let k be Kendra's age, m be Morgan's age, and l be Lizzie's age. We're given: [LIST=1] [*]k = 0.5m [*]k = l - 3 [*]k + l + m = 39 [/LIST] Rearranging (1) by multiplying each side by 2, we have: m = 2k Rearranging (2) by adding 3 to each side, we have: l = k + 3 Substituting these new values into (3), we have: k + (k + 3) + (2k) = 39 Group like terms: (k + k + 2k) + 3 = 39 4k + 3 = 39 [URL='https://www.mathcelebrity.com/1unk.php?num=4k%2B3%3D39&pl=Solve']Type this equation into the search engine[/URL], and we get: [B]k = 9 [/B] Substitute this back into (1), we have: m = 2(9) [B]m = 18 [/B] Substitute this back into (2), we have: l = (9) + 3 [B][B]l = 12[/B][/B]
Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a to
Kerry asked a bank teller to cash 390 check using 20 bills and 50 bills. If the teller gave her a total of 15 bills, how many of each type of bill did she receive? Let t = number of 20 bills and f = number of 50 bills. We have two equations. (1) 20t + 50f = 390 (2) t + f = 15 [U]Rearrange (2) into (3) for t, by subtracting f from each side:[/U] (3) t = 15 - f [U]Now substitute (3) into (1)[/U] 20(15 - f) + 50f = 390 300 - 20f + 50f = 390 [U]Combine f terms[/U] 300 + 30f = 390 [U]Subtract 300 from each side[/U] 30f = 90 [U]Divide each side by 30[/U] [B]f = 3[/B] [U]Substitute f = 3 into (3)[/U] t = 15 - 3 [B]t = 12[/B]
Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The tot
Kevin and randy have a jar containing 41 coins, all of which are either quarters or nickels. The total value of the jar is $7.85. How many of each type? Let d be dimes and q be quarters. Set up two equations from our givens: [LIST=1] [*]d + q = 41 [*]0.1d + 0.25q = 7.85 [/LIST] [U]Rearrange (1) by subtracting q from each side:[/U] (3) d = 41 - q [U]Now, substitute (3) into (2)[/U] 0.1(41 - q) + 0.25q = 7.85 4.1 - 0.1q + 0.25q = 7.85 [U]Combine q terms[/U] 0.15q + 4.1 = 7.85 [U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.15q%2B4.1%3D7.85&pl=Solve']equation calculator[/URL], we get:[/U] [B]q = 25[/B] [U]Substitute q = 25 into (3)[/U] d = 41 - 25 [B]d = 16[/B]
Kevin and Randy Muise have a jar containing 52 coins, all of which are either quarters or nickels.
Kevin and Randy Muise have a jar containing 52 coins, all of which are either quarters or nickels. The total value of the coins in the jar is $6.20. How many of each type of coin do they have? Let q be the number of quarters, and n be the number of nickels. We have: [LIST=1] [*]n + q = 52 [*]0.05n + 0.25q = 6.20 [/LIST] We can solve this system of equations three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+q+%3D+52&term2=0.05n+%2B+0.25q+%3D+6.20&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+q+%3D+52&term2=0.05n+%2B+0.25q+%3D+6.20&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+q+%3D+52&term2=0.05n+%2B+0.25q+%3D+6.20&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter what method we choose, we get the same answer: [LIST] [*][B]n = 34[/B] [*][B]q = 18[/B] [/LIST]
Kevin is 4 times old as Daniel and is also 6 years older than Daniel
Kevin is 4 times old as Daniel and is also 6 years older than Daniel. Let k be Kevin's age and d be Daniel's age. We have 2 equations: [LIST=1] [*]k = 4d [*]k = d + 6 [/LIST] Plug (1) into (2): 4d = d + 6 Subtract d from each side: 4d - d = d - d + 6 Cancel the d terms on the right side and simplify: 3d = 6 Divide each side by 3: 3d/3 = 6/3 Cancel the 3 on the left side: d = 2 Plug this back into equation (1): k = 4(2) k = 8 So Daniel is 2 years old and Kevin is 8 years old
Kevin ran 4 miles more than Steve ran. The sum of their distances is 26 miles. How far did Steve run
Kevin ran 4 miles more than Steve ran. The sum of their distances is 26 miles. How far did Steve run? The domain of the solution is: Let k be Kevin's miles ran Let s be Steve's miles ran We have 2 given equtaions: [LIST=1] [*]k = s + 4 [*]k + s = 26 [/LIST] Substitute (1) into (2) (s + 4) + s = 26 2s + 4 = 26 Plug this into our [URL='http://www.mathcelebrity.com/1unk.php?num=2s%2B4%3D26&pl=Solve']equation calculator[/URL] and we get s = 11
Kierra had $35 to spend at the movies. If it was $11 to get in and snacks were 2$ each, how many sna
Kierra had $35 to spend at the movies. If it was $11 to get in and snacks were 2$ each, how many snacks could she buy? Subtract off cover charge: 35 - 11 = 24 Let s equal the number of snacks Kierra can buy. With each snack costing $2, we have the following equation: 2s = 24 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2s%3D24&pl=Solve']equation calculator[/URL], we have: [B]s = 12[/B]
Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What
Kiko is now 6 times as old as his sister. In 6 years, he will be 3 times as old as his sister. What is their present age? Let k be Kiko's present age Let s be Kiko's sisters age. We're given two equations: [LIST=1] [*]k = 6s [*]k + 6 = 3(s + 6) [/LIST] To solve this system of equations, we substitute equation (1) into equation (2) for k: 6s + 6 = 3(s + 6) [URL='https://www.mathcelebrity.com/1unk.php?num=6s%2B6%3D3%28s%2B6%29&pl=Solve']Typing this equation into our math engine[/URL] to solve for s, we get: s = [B]4[/B] To solve for k, we substitute s = 4 into equation (1) above: k = 6 * 4 k = [B]24[/B]
kim and jason just had business cards made. kim�s printing company charged a one time setup fee of $
kim and jason just had business cards made. kim�s printing company charged a one time setup fee of $8 and then $20 per box of cards. jason,meanwhile ordered his online. they cost $8 per box. there was no setup fee, but he had to pay $20 to have his order shipped to his house. by coincidence, kim and jason ended up spending the same amount on their business cards. how many boxes did each buy? how much did each spend? Set up Kim's cost function C(b) where b is the number of boxes: C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee C(b) = 20c + 8 + 0 Set up Jason's cost function C(b) where b is the number of boxes: C(b) = Cost per box * number of cards + Setup Fee + Shipping Fee C(b) = 8c + 0 + 20 Since Kim and Jason spent the same amount, set both cost equations equal to each other: 20c + 8 = 8c + 20 [URL='https://www.mathcelebrity.com/1unk.php?num=20c%2B8%3D8c%2B20&pl=Solve']Type this equation into our search engine[/URL] to solve for c, and we get: c = 1 How much did they spend? We pick either Kim's or Jason's cost equation since they spent the same, and plug in c = 1: Kim: C(1) = 20(1) + 8 C(1) = 20 + 8 C(1) = [B]28 [/B] Jason: C(1) = 8(1) + 20 C(1) = 8 + 20 C(1) = [B]28[/B]
Kim earns $30 for babysitting on Friday nights. She makes an average of $1.25 in tips per hour. Writ
Kim earns $30 for babysitting on Friday nights. She makes an average of $1.25 in tips per hour. Write the function of Kim's earnings, and solve for how much she would make after 3 hours. Set up the earnings equation E(h) where h is the number of hours. We have the function: E(h) = 1.25h + 30 The problem asks for E(3): E(3) = 1.25(3) + 30 E(3) = 4.75 + 30 E(3) = [B]$34.75[/B]
Kimberly takes 4 pages of notes during each hour of class. Write an equation that shows the relation
Kimberly takes 4 pages of notes during each hour of class. Write an equation that shows the relationship between the time in class x and the number of pages y. With x hours and y pages, our equation is: [B]y = 4x [/B]
Kimberly wants to become a member of the desert squad at a big catering company very badly, but she
Kimberly wants to become a member of the desert squad at a big catering company very badly, but she must pass three difficult tests to do so. On the first Terrifying Tiramisu test she scored a 68. On the second the challenging Chocalate-Sprinkled Creme Brulee she scored a 72. If kimberly needs an average of 60 on all three tests to become a member on the squad what is the lowest score she can make on her third and final test This is a missing average problem. Given 2 scores of 68, 72, what should be score number 3 in order to attain an average score of 60? [SIZE=5][B]Setup Average Equation:[/B][/SIZE] Average = (Sum of our 2 numbers + unknown score of [I]x)/[/I]Total Numbers 60 = (68 + 72 + x)/3 [SIZE=5][B]Cross Multiply[/B][/SIZE] 68 + 72 + x = 60 x 3 x + 140 = 180 [SIZE=5][B]Subtract 140 from both sides of the equation to isolate x:[/B][/SIZE] x + 140 - 140 = 180 - 140 x = [B]40[/B]
Kinematic Equations
Given the 5 inputs of the 4 kinematic equations, this will solve any of the equations it can based on your inputs for the kinematics.
Kinetic Energy
Solves for any of the 3 items in the kinetic energy equation: Energy (e), Mass (m), and Velocity (v)
Kristen and Julia went skating. Julia skated 30 minutes longer than Kristen. If Julia skated for 55
Kristen and Julia went skating. Julia skated 30 minutes longer than Kristen. If Julia skated for 55 minutes, write and solve an equation to find how long Kristen skated Let j be the number of minutes Julia skates and k be the number of minutes Kristen skated. We have 2 equations: [B](1) j = k + 30 (2) j = 55[/B] [U]Plug (2) into (1)[/U] j = 55 + 30 [B]j = 85 minutes, or 1 hour and 25 minutes[/B]
Krutika was thinking of a number. Krutika doubles it and adds 8.7 to get an answer of 64.9. Form an
Krutika was thinking of a number. Krutika doubles it and adds 8.7 to get an answer of 64.9. Form an equation with x from the information. [LIST=1] [*]The number we start with is x. [*]Double it means we multiply by 2: 2x [*]Add 8.7: 2x + 8.7 [*][I]Get an answer[/I] means we have an equation, so we set (3) above equal to 64.9 [*][B]2x + 8.7 = 64.9[/B] [/LIST] If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B8.7%3D64.9&pl=Solve']equation calculator[/URL].
kyle baked 29 muffins. He placed p muffins each in 4 boxes and had 5 muffins left over. How many muf
kyle baked 29 muffins. He placed p muffins each in 4 boxes and had 5 muffins left over. How many muffins were in each box We set up the following equation: 4p + 5 = 29 To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=4p%2B5%3D29&pl=Solve']type it in our math engine[/URL] and we get: p = [B]6[/B]
larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2
larger of 2 numbers is 12 more than the smaller number. if the sum of the 2 numbers is 74 find the 2 numbers Declare Variables for each number: [LIST] [*]Let l be the larger number [*]Let s be the smaller number [/LIST] We're given two equations: [LIST=1] [*]l = s + 12 [*]l + s = 74 [/LIST] Equation (1) already has l solved for. Substitute equation (1) into equation (2) for l: s + 12 + s = 74 Solve for [I]s[/I] in the equation s + 12 + s = 74 [SIZE=5][B]Step 1: Group the s terms on the left hand side:[/B][/SIZE] (1 + 1)s = 2s [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 2s + 12 = + 74 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 12 and 74. To do that, we subtract 12 from both sides 2s + 12 - 12 = 74 - 12 [SIZE=5][B]Step 4: Cancel 12 on the left side:[/B][/SIZE] 2s = 62 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2s/2 = 62/2 s = [B]31[/B] To solve for l, we substitute in s = 31 into equation (1): l = 31 + 12 l = [B]43[/B]
larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number?
larger of 2 numbers is 4 more than the smaller. the sum of the 2 is 40. what is the larger number? Declare variables for the 2 numbers: [LIST] [*]Let l be the larger number [*]Let s be the smaller number [/LIST] We're given two equations: [LIST=1] [*]l = s + 4 [*]l + s = 40 [/LIST] To get this problem in terms of the larger number l, we rearrange equation (1) in terms of l. Subtract 4 from each side in equation (1) l - 4 = s + 4 - 4 Cancel the 4's and we get: s = l - 4 Our given equations are now: [LIST=1] [*]s = l - 4 [*]l + s = 40 [/LIST] Substitute equation (1) into equation (2) for s: l + l - 4 = 40 Grouping like terms for l, we get: 2l - 4 = 40 Add 4 to each side: 2l - 4 + 4 = 40 + 4 Cancelling the 4's on the left side, we get 2l = 44 Divide each side of the equation by 2 to isolate l: 2l/2 = 44/2 Cancel the 2's on the left side and we get: l = [B]22[/B]
Larry is buying new clothes for his return to school. He is buying shoes for $57 and shirts cost $15
Larry is buying new clothes for his return to school. He is buying shoes for $57 and shirts cost $15 each. He has $105 to spend. Which of the following can be solved to find the number of shirts he can afford? Let s be the number of shirts. Since shoes are a one-time fixed cost, we have: 15s + 57 = 105 We want to solve this equation for s. We [URL='https://www.mathcelebrity.com/1unk.php?num=15s%2B57%3D105&pl=Solve']type it in our math engine[/URL] and we get: s = [B]3.2 or 3 whole shirts[/B]
Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7%
Larry Mitchell invested part of his $31,000 advance at 6% annual simple interest and the rest at 7% annual simple interest. If the total yearly interest from both accounts was $2,090, find the amount invested at each rate. Let x be the amount invested at 6%. Then 31000 - x is invested at 7%. We have the following equation: 0.06x + (31000 - x)0.07 = 2090 Simplify: 0.06x + 2170 - 0.07x = 2090 Combine like Terms -0.01x + 2170 = 2090 Subtract 2170 from each side -0.01x = -80 Divide each side by -0.01 x = [B]8000 [/B]at 6% Which means at 7%, we have: 31000 - 8000 = [B]23,000[/B]
Last week at the business where you work, you sold 120 items. The business paid $1 per item and sol
Last week at the business where you work, you sold 120 items. The business paid $1 per item and sold them for $3 each. What profit did the business make from selling the 120 items? Let n be the number of items. We have the following equations: Cost Function C(n) = n For n = 120, we have C(120) = 120 Revenue Function R(n) = 3n For n = 120, we have R(120) = 3(120) = 360 Profit = Revenue - Cost Profit = 360 - 120 Profit = [B]240[/B]
Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this
Lauren wrote a total of 6 pages over 2 hours. How many hours will Lauren have to spend writing this week in order to have written a total of 9 pages? Solve using unit rates. 6 pages per 2 hours equals 6/2 = 3 pages per hour as a unit rate Set up equation using h hours: 3h = 9 Divide each side by 3 [B]h = 3[/B]
Lauren's savings increased by 12 and is now 31
Lauren's savings increased by 12 and is now 31 [LIST] [*]Let Lauren's savings be s. [*]The phrase increased by means we add. [*]The phrase [I]is now[/I] means an equation. [*]We have an algebraic expression of: [/LIST] [B]s + 12 = 31 [/B] To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=s%2B12%3D31&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]19[/B]
Lebron James scored 288 points in 9 games this season. Assuming he continues to score at this consta
Lebron James scored 288 points in 9 games this season. Assuming he continues to score at this constant rate, write a linear equation that represents the scenario. 288 points / 9 games = 32 points per game Let g be the number of games Lebron plays. We build an equation for his season score: Lebron's Season Score = Points per game * number of games Lebron's Season Score = [B]32g[/B]
Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI
Lily needs an internet connectivity package for her firm. She has a choice between CIVISIN and GOMI with the following monthly billing policies. Each company's monthly billing policy has an initial operating fee and charge per megabyte. Operating Fee charge per Mb CIVSIN 29.95 0.14 GOMI 4.95 0.39 (i) Write down a system of equations to model the above situation (ii) At how many Mb is the monthly cost the same? What is the equal monthly cost of the two plans? (i) Set up a cost function C(m) for CIVSIN where m is the number of megabytes used: C(m) = charge per Mb * m + Operating Fee [B]C(m) = 0.14m + 29.95[/B] Set up a cost function C(m) for GOMI where m is the number of megabytes used: C(m) = charge per Mb * m + Operating Fee [B]C(m) = 0.39m + 4.95 [/B] (ii) At how many Mb is the monthly cost the same? Set both cost functions equal to each other: 0.14m + 29.95 = 0.39m + 4.95 We [URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B29.95%3D0.39m%2B4.95&pl=Solve']type this equation into our search engine[/URL] and we get: m = [B]100[/B] (ii) What is the equal monthly cost of the two plans? CIVSIN - We want C(100) from above where m = 100 C(100) = 0.14(100) + 29.95 C(100) = 14 + 29.95 C(100) = [B]43.95[/B] GOMI - We want C(100) from above where m = 100 C(100) = 0.39(100) + 4.95 C(100) = 39 + 4.95 C(100) = [B]43.95[/B]
Linda takes classes at both Westside Community College and Pinewood Community College. At Westside,
Linda takes classes at both Westside Community College and Pinewood Community College. At Westside, class fees are $98 per credit hour, and at Pinewood, class fees are $115 per credit hour. Linda is taking a combined total of 18 credit hours at the two schools. Suppose that she is taking w credit hours at Westside. Write an expression for the combined total dollar amount she paid for her class fees. Let p be the number of credit hours at Pinewood. We have two equations: [LIST] [*]98w for Westside [*]115p at Pinewood [*]w + p = 18 [*]Total fees: [B]98w + 115p[/B] [/LIST]
Line Equation-Slope-Distance-Midpoint-Y intercept
Enter 2 points, and this calculates the following:
* Slope of the line (rise over run) and the line equation y = mx + b that joins the 2 points
* Midpoint of the two points
* Distance between the 2 points
* 2 remaining angles of the rignt triangle formed by the 2 points
* y intercept of the line equation
* Point-Slope Form
* Parametric Equations and Symmetric Equations
Or, if you are given a point on a line and the slope of the line including that point, this calculates the equation of that line and the y intercept of that line equation, and point-slope form.
Also allows for the entry of m and b to form the line equation
Linear Congruence
Given an modular equation ax ≡ b (mod m), this solves for x if a solution exists
Literal Equations
Solves literal equations with no powers for a variable of your choice as well as open sentences.
Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes.
Liz harold has a jar in her office that contains 47 coins. Some are pennies and the rest are dimes. If the total value of the coins is 2.18, how many of each denomination does she have? [U]Set up two equations where p is the number of pennies and d is the number of dimes:[/U] (1) d + p = 47 (2) 0.1d + 0.01p = 2.18 [U]Rearrange (1) into (3) by solving for d[/U] (3) d = 47 - p [U]Substitute (3) into (2)[/U] 0.1(47 - p) + 0.01p = 2.18 4.7 - 0.1p + 0.01p = 2.18 [U]Group p terms[/U] 4.7 - 0.09p = 2.18 [U]Add 0.09p to both sides[/U] 0.09p + 2.18 = 4.7 [U]Subtract 2.18 from both sides[/U] 0.09p = 2.52 [U]Divide each side by 0.09[/U] [B]p = 28[/B] [U]Now substitute that back into (3)[/U] d =47 - 28 [B]d = 19[/B]
Local salesman receives a base salary of $650 monthly. He also receives a commission of 11% on all s
Local salesman receives a base salary of $650 monthly. He also receives a commission of 11% on all sales over $1500. How much would he have to sell in one month if he needed to have $3000 Let the Sales amount be s. We have: Sales over 1,500 is written as s - 1500 11% is also 0.11 as a decimal, so we have: 0.11(s - 1500) + 650 = 3000 Multiply through: 0.11s - 165 + 650 = 3500 0.11s + 485 = 3500 To solve this equation for s, [URL='https://www.mathcelebrity.com/1unk.php?num=0.11s%2B485%3D3500&pl=Solve']we type it in our search engine[/URL] and we get: s = [B]27,409.10[/B]
Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nep
Logan is 8 years older than 4 times the age of his nephew. Logan is 32 years old. How old is his nephew? Let the age of Logan's nephew be n. We're given: 4n + 8 = 32 (Since [I]older[/I] means we add) To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=4n%2B8%3D32&pl=Solve']type it into our search engine[/URL] and we get: [B]n = 6[/B]
Logarithms
Using the formula Log ab = e, this calculates the 3 pieces of a logarithm equation:
1) Base (b)
2) Exponent
3) Log Result
In addition, it converts
* Expand logarithmic expressions
Logarithms and Natural Logarithms and Eulers Constant (e)
This calculator does the following:
* Takes the Natural Log base e of a number x Ln(x) → logex
* Raises e to a power of y, ey
* Performs the change of base rule on logb(x)
* Solves equations in the form bcx = d where b, c, and d are constants and x is any variable a-z
* Solves equations in the form cedx=b where b, c, and d are constants, e is Eulers Constant = 2.71828182846, and x is any variable a-z
* Exponential form to logarithmic form for expressions such as 53 = 125 to logarithmic form
* Logarithmic form to exponential form for expressions such as Log5125 = 3
Lorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are t
Lorda is older than Kate. The sum of their ages is 30. The difference in their ages is 6. What are their ages? Let Lorda's age be l. Let Kate's age be k. We're given two equations: [LIST=1] [*]l + k = 30 [*]l - k = 6 <-- Since Lorda is older [/LIST] Add the 2 equations together and we eliminate k: 2l = 36 [URL='https://www.mathcelebrity.com/1unk.php?num=2l%3D36&pl=Solve']Typing this equation into our search engine[/URL] and solving for l, we get: l = [B]18[/B] Now substitute l = 18 into equation 1: 18 + k = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=18%2Bk%3D30&pl=Solve']Type this equation into our search engine[/URL] and solving for k, we get: k = [B]12[/B]
m is the midpoint of cf for points c(3,4) and f(9,8). Find MF
m is the midpoint of cf for points c(3,4) and f(9,8). Find MF Using our [URL='https://www.mathcelebrity.com/slope.php?xone=3&yone=4&slope=+2%2F5&xtwo=9&ytwo=8&pl=You+entered+2+points']line equation and midpoint calculator[/URL], we get: MF = [B](6, 6)[/B]
M is the sum of a and its reciprocal
M is the sum of a and its reciprocal The reciprocal of a variable is 1 divided by the variable 1/a The sum of a and its reciprocal means we add: a + 1/a The phrase [I]is[/I] means an equation, so we set M equal to the sum of a + 1/a: [B]M = 1 + 1/a[/B]
M/n = p-6 for m
M/n = p-6 for m Solve this literal equation by multiplying each side by n to isolate M: Mn/n = n(p - 6) Cancelling the n terms on the left side, we get: [B]M = n(p - 6)[/B]
m/x = k-6 for m
m/x = k-6 for m To solve this literal equation, multiply each side by x: x(m/x) = x(k - 6) The x's cancel on the left side, so we get: m = [B]x(k - 6)[/B]
Maggie earns $10 each hour she works at the pet store and $0.25 for each phone call she answers. Mag
Maggie earns $10 each hour she works at the pet store and $0.25 for each phone call she answers. Maggie answered 60 phone calls and earned $115 last week Set up an equation where c is the number of phone calls Maggie answers and h is the number of hours Maggie worked: 0.25c + 10h = 115 We're given c = 60, so we have: 0.25(60) + 10h = 115 15 + 10h = 115 We want to solve for h. So we[URL='https://www.mathcelebrity.com/1unk.php?num=15%2B10h%3D115&pl=Solve'] type this equation into our search engine[/URL] and we get: h = [B]10[/B]
maggie has two job offers. The first job offers to pay her $50 per week and 10 1/2 cents per flier.
maggie has two job offers. The first job offers to pay her $50 per week and 10 1/2 cents per flier. The second job offer will pay only $30 per week but gives 20 cents per flier. Write and solve an equation to find how many fliers must she deliver so that the two offers pay the same per week? Let the number of fliers be f. First job: 0.105f + 50 Second job: 20f + 30 Set them equal to each other: 0.105f + 50 = 20f + 30 [URL='https://www.mathcelebrity.com/1unk.php?num=0.105f%2B50%3D20f%2B30&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]f = 1[/B]
Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of
Marco takes 2 quizzes each week. Write an equation that shows the relationship between the number of weeks x and the total number of quizzes y. Write your answer as an equation with y first, followed by an equals sign. Our total quizzes equal 2 times the number of weeks (x): [B]y = 2x[/B]
Marginal propensity to save is 0.3. Calculate MPC
Marginal propensity to save is 0.3. Calculate MPC. MPC is Marginal Propensity to Consume. And MPS is Marginan Propensity to Save. The relational equation between the two is: MPC + MPS = 1 To get MPC, we have: MPC = 1 - MPS The problem gives us MPS = 0.3, so plug it into this modified MPC equation: MPC = 1 - 0.3 MPC = [B]0.7[/B]
Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now
Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. How many did she start with? Take this in parts [LIST=1] [*]Maria starts with b boxes. [*]She buys seven more. So she has b + 7 boxes [*]A week later, half of all her boxes are destroyed in a fire. Which means she's left with 1/2. (b + 7)/2 [*]Now she has 22 boxes. So we set (b + 7)/2 = 22 [/LIST] (b + 7)/2 = 22 Cross multiply: b + 7 = 22 * 2 b + 7 = 44 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Typing this equation into our search engine and solving for b[/URL], we get: [B]b = 37[/B]
Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now
Maria bought seven boxes. A week later half of all her boxes were destroyed in a fire. There are now only 22 boxes left. With how many did she start? Let the number of boxes Maria started with be b. We're given the following pieces: [LIST] [*]She starts with b [*]She bought 7 boxes. So we add 7 to b: b + 7 [*]If half the boxes were destroyed, she's left with 1/2. So we divide (b + 7)/2 [*]Only 22 boxes left means we set (b + 7)/2 equal to 22 [/LIST] (b + 7)/2 = 22 Cross multiply: b + 7 = 22 * 2 b + 7 = 44 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B7%3D44&pl=Solve']Type this equation into our search engine[/URL] to solve for b and we get: b = [B]37[/B]
Maria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each w
Maria is saving money to buy a bike that cost 133$. She has 42$ and will save an additional 7 each week. Set up an equation with w as the number of weeks. We want to find w such that: 7w + 42 = 133 [URL='https://www.mathcelebrity.com/1unk.php?num=7w%2B42%3D133&pl=Solve']Typing this equation into our search engine[/URL], we get: w = [B]13[/B]
Marissa has 24 coins in quarters and nickels. She has 3 dollars. How many of the coins are quarters?
Let n be the number of nickels and q be the number of quarters. We have two equations: (1) n + q = 24 (2) 0.05n + 0.25q = 3 Rearrange (1) to solve for n in terms of q for another equation (3) (3) n = 24 - q Plug (3) into (2) 0.05(24 - q) + 0.25q = 3 Multiply through: 1.2 - 0.05q + 0.25q = 3 Combine q terms 0.2q + 1.2 = 3 Subtract 1.2 from each side: 0.2q = 1.8 Divide each side by 0.2 [B]q = 9[/B]
Mark and Jennie are bowling. Jennie�s score is double Mark�s score. If the sum of their score is 171
Mark and Jennie are bowling. Jennie�s score is double Mark�s score. If the sum of their score is 171, find each person�s score by writing out an equation. Let Mark's score be m. Let Jennie's score be j. We're given two equations: [LIST=1] [*]j = 2m [*]j + m = 171 [/LIST] Substitute equation (1) into equation (2): 2m + m = 171 [URL='https://www.mathcelebrity.com/1unk.php?num=2m%2Bm%3D171&pl=Solve']Type this equation into our search engine[/URL] to solve for m: m = [B]57 [/B] To solve for j, we substitute m = 57 in equation (1) above: j = 2(57) j = [B]114[/B]
Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bik
Marla wants to rent a bike Green Lake Park has an entrance fee of $8 and charges $2 per hour for bike Oak Park has an entrance fee of $2 and charges $5 per hour for bike rentals she wants to know how many hours are friend will make the costs equal [U]Green Lake Park: Set up the cost function C(h) where h is the number of hours[/U] C(h) = Hourly Rental Rate * h + Entrance Fee C(h) = 2h + 8 [U]Oak Park: Set up the cost function C(h) where h is the number of hours[/U] C(h) = Hourly Rental Rate * h + Entrance Fee C(h) = 5h + 2 [U]Marla wants to know how many hours make the cost equal, so we set Green Lake Park's cost function equal to Oak Parks's cost function:[/U] 2h + 8 = 5h + 2 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=2h%2B8%3D5h%2B2&pl=Solve']type this equation into our search engine[/URL] and we get: h = [B]2[/B]
Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find t
Martha is 18 years older than Harry. Their ages add to 106. Write an equation and solve it to find the ages of Martha and Harry. Let m be Martha's age. Let h be Harry's age. We're given two equations: [LIST=1] [*]m = h + 18 [I](older means we add)[/I] [*]h + m = 106 [/LIST] Substitute equation (1) into equation (2) for m: h + h + 18 = 106 To solve for h, [URL='https://www.mathcelebrity.com/1unk.php?num=h%2Bh%2B18%3D106&pl=Solve']we type this equation into our search engine[/URL] and we get: h = [B]44[/B]
Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than
Marty is 3 years younger than 6 times his friend Warrens age. The sum of their ages is greater than 11. What is the youngest age Warren can be? Let m be Marty's age and w be Warren's age. We have two equations: (1) m = 6w - 3 (2) m + w > 11 Plug (1) into (2) 6w - 3 + w > 11 Combine w terms 7w - 3 > 11 Add 3 to each side 7w > 14 Divide each side by 7 w > 2 which means [B]w = 3[/B] as the youngest age.
Mary went bowling on the weekend. Each game cost $2.50, and the shoe rental $2.00. She spent $14.50
Mary went bowling on the weekend. Each game cost $2.50, and the shoe rental $2.00. She spent $14.50 total. How many games did she bowl? Set up the equation where g is the number of games. We add the shoe rental fee to the cost per games 2.5g + 2 = 14.50 To solve for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5g%2B2%3D14.50&pl=Solve']type this equation into our search engine[/URL] and we get: g = [B]5[/B]
Matilda needs at least $112 to buy an new dress. She has already saved $40. She earns $9 an hour bab
Matilda needs at least $112 to buy an new dress. She has already saved $40. She earns $9 an hour babysitting. Write and solve and inequality to find how many hours she will need to babysit to buy the dress. Subtract remaining amount needed after savings: 112 - 40 = 72 Let h be her hourly wages for babysitting. We have the equation: [B]9h = 72[/B] Divide each side by 9 [B]h = 8[/B]
Matrix Properties
Given a matrix |A|, this calculates the following items if they exist:
* Determinant = det(A)
* Inverse = A-1
* Transpose = AT
* Adjoint = adj(A)
* Eigen equation (characteristic polynomial) = det|λI - A|
* Trace = tr(A)
* Gauss-Jordan Elimination using Row Echelon and Reduced Row Echelon Form
* Dimensions of |A| m x n
* Order of a matrix
* Euclidean Norm ||A||
* Magic Sum if it exists
* Determines if |A| is an Exchange Matrix
Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking ac
Matt has $100 dollars in a checking account and deposits $20 per month. Ben has $80 in a checking account and deposits $30 per month. Will the accounts ever be the same balance? explain Set up the Balance account B(m), where m is the number of months since the deposit. Matt: B(m) = 20m + 100 Ben: B(m) = 80 + 30m Set both balance equations equal to each other to see if they ever have the same balance: 20m + 100 = 80 + 30m To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=20m%2B100%3D80%2B30m&pl=Solve']we type this equation into our search engine[/URL] and we get: m = [B]2 So yes, they will have the same balance at m = 2[/B]
Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00 bob bought 3 burgers and
Max and Bob went to the store. Max bought 2 burgers and 2 drinks for $5.00. Bob bought 3 burgers and 1 drink for $5.50. How much is each burger and drink? [U]Set up the givens where b is the cost of a burger and d is the cost of a drink:[/U] Max: 2b + 2d = 5 Bob: 3b + d = 5.50 [U]Rearrange Bob's equation by subtracting 3b from each side[/U] (3) d = 5.50 - 3b [U]Now substitute that d equation back into Max's Equation[/U] 2b + 2(5.50 - 3b) = 5 2b + 11 - 6b = 5 [U]Combine b terms:[/U] -4b + 11 = 5 [U]Subtract 11 from each side[/U] -4b = -6 [U]Divide each side by -4[/U] b = 3/2 [B]b = $1.50[/B] [U]Now plug that back into equation (3):[/U] d = 5.50 - 3(1.50) d = 5.50 - 4.50 [B]d = $1.00[/B]
Max is 23 years younger than his father.Together their ages add up to 81.
Max is 23 years younger than his father.Together their ages add up to 81. Let Max's age be m, and his fathers' age be f. We're given: [LIST=1] [*]m = f - 23 <-- younger means less [*]m + f = 81 [/LIST] Substitute Equation (1) into (2): (f - 23) + f = 81 Combine like terms to form the equation below: 2f - 23 = 81 [URL='https://www.mathcelebrity.com/1unk.php?num=2f-23%3D81&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]f = 52[/B] Substitute this into Equation (1): m = 52 - 23 [B]m = 29[/B]
Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad?
Max's age is 2 more than his fathers age divided by 4. Max is 13 years old. How old is his dad? Let Max's father be age f. We're given: (f + 2)/4 = 13 Cross Multiply: f + 2 = 52 [URL='https://www.mathcelebrity.com/1unk.php?num=f%2B2%3D52&pl=Solve']Typing this equation into the search engine[/URL], we get: f = [B]50[/B]
Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many
Megan has $50 and saves $5.50 each week. Connor has $18.50 and saves $7.75 each week. After how many weeks will megan and connor have saved the same amount [U]Set up the Balance function B(w) where w is the number of weeks for Megan:[/U] B(w) = savings per week * w + Current Balance B(w) = 5.50w + 50 [U]Set up the Balance function B(w) where w is the number of weeks for Connor:[/U] B(w) = savings per week * w + Current Balance B(w) = 7.75w + 18.50 The problem asks for w when both B(w) are equal. So we set both B(w) equations equal to each other: 5.50w + 50 = 7.75w + 18.50 To solve this equation for w, we[URL='https://www.mathcelebrity.com/1unk.php?num=5.50w%2B50%3D7.75w%2B18.50&pl=Solve'] type it in our search engine[/URL] and we get: w = [B]14[/B]
Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she c
Melissa runs a landscaping business. She has equipment and fuel expenses of $264 per month. If she charges $53 for each lawn, how many lawns must she service to make a profit of at $800 a month? Melissa has a fixed cost of $264 per month in fuel. No variable cost is given. Our cost function is: C(x) = Fixed Cost + Variable Cost. With variable cost of 0, we have: C(x) = 264 The revenue per lawn is 53. So R(x) = 53x where x is the number of lawns. Now, profit is Revenue - Cost. Our profit function is: P(x) = 53x - 264 To make a profit of $800 per month, we set P(x) = 800. 53x - 264 = 800 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=53x-264%3D800&pl=Solve']equation solver[/URL], we get: [B]x ~ 21 lawns[/B]
Michelle and Julie sold 65 cupcakes. If Julie sold 9 more cupcakes than Michelle, how many cupcakes
Michelle and Julie sold 65 cupcakes. If Julie sold 9 more cupcakes than Michelle, how many cupcakes did each of them sell? Let m = Michelle's cupcakes and j = Julie's cupcakes. We have two equations: m + j = 65 j = m + 9 Substituting, we get: m + (m + 9) = 65 Combine like terms, we get: 2m + 9 = 65 Subtract 9 from each side: 2m = 56 Divide each side by 2 to isolate m m = 28 If m = 28, then j = 28 + 9 = 37 So (m, j) = (28, 37)
mike went to canalside with $40 to spend. he rented skates for $10 and paid $3 per hour to skate.wha
mike went to canalside with $40 to spend. he rented skates for $10 and paid $3 per hour to skate.what is the greatest number of hours Mike could have skated? Let h be the number of hours of skating. We have the cost function C(h): C(h) = Hourly skating rate * h + rental fee C(h) = 3h + 10 The problem asks for h when C(h) = 40: 3h + 10 = 40 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=3h%2B10%3D40&pl=Solve']type it in our search engine[/URL] and we get: h = [B]10[/B]
Mike works in a toy store. One week, he worked 38 hours and made $220. The next week, he received a
Mike works in a toy store. One week, he worked 38 hours and made $220. The next week, he received a raise, so when he worked 30 hours he made $180. How much was his raise (to the nearest cent)? First week, Mike earns the following in hours (h) 38h = 220 h = 5.79 [URL='https://www.mathcelebrity.com/1unk.php?num=38h%3D220&pl=Solve']using our equation calculator[/URL] We call this his old hourly salary Next week, Mike earns the following in hours (h) 30h = 180 h = 6 [URL='https://www.mathcelebrity.com/1unk.php?num=30h%3D180&pl=Solve']using our equation calculator[/URL] We call this his new hourly salary His raise is the difference between his current hourly salary and his old hourly salary: Raise = New Hourly Salary - Old Hourly Salary Raise = 6 - 5.79 Raise = [B]$0.21[/B] Mike got a 21 cent hourly raise
Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies
Milan plans to watch 2 movies each month. Write an equation to represent the total number of movies n that he will watch in m months. Number of movies equals movies per month times the number of months. So we have: [B]n = 2m[/B]
Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake troy had 1/4 of
Mindy and troy combined ate 9 pieces of the wedding cake. Mindy ate 3 pieces of cake troy had 1/4 of the total cake. Write an equation to determine how many pieces of cake (c) that were in total Let c be the total number of pieces of cake. Let m be the number of pieces Mindy ate. Let t be the number of pieces Troy ate. We have the following given equations: [LIST] [*]m + t = 9 [*]m = 3 [*]t = 1/4c [/LIST] Combining (2) and (3) into (1), we have: 3 + 1/4c = 9 Subtract 3 from each side: 1/4c = 6 Cross multiply: [B]c = 24[/B]
Molly is making strawberry infused water. For each ounce of strawberry juice, she uses two times as
Molly is making strawberry infused water. For each ounce of strawberry juice, she uses three times as many ounces of water as juice. How many ounces of strawberry juice and how many ounces of water does she need to make 40 ounces of strawberry infused water? Let j be the ounces of strawberry juice and w be the ounces of water. We're given: [LIST=1] [*]j + w = 40 [*]w = 3j [/LIST] Substitute (2) into (1): j + 3j = 40 Combine like terms: 4j = 40 [URL='https://www.mathcelebrity.com/1unk.php?num=4j%3D40&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]j = 10[/B] From equation (2), we substitute j = 2: w = 3(10) [B]w = 30 [/B] This means we have [B]10 ounces of juice[/B] and [B]30 ounces of water[/B] for a 40 ounce mix.
Moment of Inertia
Calculates any of the 3 items from the Moment of Inertia equation, Inertia (I), Mass (M), and Length (L).
Mr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paid
Mr turner sent his car to the workshop for repair work as well as to change 4 tires. Mr turner paid $1035 in all. The repair work cost 5 times the price of each tire. The mechanic told Mr. turner that the repair work cost $500. Explain the mechanic�s mistake Let the cost for work be w. Let the cost for each tire be t. We're given; [LIST=1] [*]w = 5t [*]w + 4t = 1035 [/LIST] Substitute equation 1 into equation 2: (5t) + 4t = 1035 [URL='https://www.mathcelebrity.com/1unk.php?num=%285t%29%2B4t%3D1035&pl=Solve']Type this equation into our search engine[/URL], and we get: t = 115 Substitute this into equation (1): w = 5(115) w = [B]575[/B] The mechanic underestimated the work cost.
Mr. Chris�s new app �Tick-Tock� is the hottest thing to hit the app store since...ever. It costs $5
Mr. Chris�s new app �Tick-Tock� is the hottest thing to hit the app store since...ever. It costs $5 to buy the app and then $2.99 for each month that you subscribe (a bargain!). How much would it cost to use the app for one year? Write an equation to model this using the variable �m� to represent the number of months that you use the app. Set up the cost function C(m) where m is the number of months you subscribe: C(m) = Monthly Subscription Fee * months + Purchase fee [B]C(m) = 2.99m + 5[/B]
Mr. Demerath has a large collection of Hawaiian shirts. He currently has 42 Hawaiian shirts. He gets
Mr. Demerath has a large collection of Hawaiian shirts. He currently has 42 Hawaiian shirts. He gets 2 more every month. After how many months will Mr. Demerath have at least 65 Hawaiian shirts? We set up the function H(m) where m is the number of months that goes by. Mr. Demerath's shirts are found by: H(m) = 2m + 42 The problem asks for m when H(m) = 65. So we set H(m) = 65: 2m + 42 = 65 To solve this equation for m, we[URL='https://www.mathcelebrity.com/1unk.php?num=2m%2B42%3D65&pl=Solve'] type it in our search engine [/URL]and we get: m = [B]11.5[/B]
Mr. Wilson wants to park his carin a parking garage that charges 3 per hour along with a flat fee of
Mr. Wilson wants to park his carin a parking garage that charges 3 per hour along with a flat fee of 6. If Mr. Wilson paid 54 to park in the garage, for how many hours did he park there? [U]Set up an equation, where f is the flat fee, and h is the number of hours parked:[/U] 3h + f = 54 [U]Substitute f = 6 into the equation:[/U] 3h + 6 = 54 [U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3h%2B6%3D54&pl=Solve']equation solver[/URL], we get[/U] [B]h = 16[/B]
Mr. Winkle downloaded 34 more songs than Mrs. Winkle downloaded. Together they downloaded 220 song
Mr. Winkle downloaded 34 more songs than Mrs. Winkle downloaded. Together they downloaded 220 songs. How many songs did each download? Let x = Mr. Winkle downloads and y = Mrs. Winkle downloads. We then have x = y + 34 and x + y = 220. Substitute equation 1 into equation 2, we have: (y + 34) + y = 220 2y + 34 = 220 Subtract 34 from each side: 2y = 186 Divide each side by 2: y = 93 (Mrs. Winkle) x = 93 + 34 x = 127 (Mr. Winkle)
Mrs. Lowe charges $45 an hour with a $10 flat fee for tutoring. Mrs. Smith charges $40 an hour wit
Mrs. Lowe charges $45 an hour with a $10 flat fee for tutoring. Mrs. Smith charges $40 an hour with a $15 flat fee to tutor. Write an equation that represents the situation when the cost is the same to be tutored by Mrs. Lowe and Mrs. Smith. [U]Set up cost equation for Mrs. Lowe where h is the number of hours tutored:[/U] Cost = Hourly Rate * number of hours + flat fee Cost = 45h + 10 [U]Set up cost equation for Mrs. Smith where h is the number of hours tutored:[/U] Cost = Hourly Rate * number of hours + flat fee Cost = 40h + 15 [U]Set both cost equations equal to each other:[/U] 45h + 10 = 40h + 15 <-- This is our equation To solve for h if the problem asks, we [URL='https://www.mathcelebrity.com/1unk.php?num=45h%2B10%3D40h%2B15&pl=Solve']type this equation into our search engine[/URL] and we get: h = 1
Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest
Ms. Jeffers is splitting $975 among her three sons. If the oldest gets twice as much as the youngest and the middle son gets $35 more than the youngest, how much does each boy get? Let 0 be the oldest son, m be the middle sun, and y be the youngest son. Set up our given equations [LIST] [*]o = 2y [*]m = y + 35 [*]o + m + y = 975 [/LIST] [U]Substitute the first and second equations into Equation 3[/U] 2y + y + 35 + y = 975 [U]Combine the y terms[/U] 4y + 35 = 975 Subtract 35 using our [URL='http://www.mathcelebrity.com/1unk.php?num=4y%2B35%3D975&pl=Solve']equation calculator[/URL] to solve and get [B]y = 235[/B] [U]Plug y = 235 into equation 2[/U] m = 235 + 35 [B]m = 270[/B] [U]Plug y = 235 into equation 2[/U] o = 2(235) [B]o = 470[/B]
Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and su
Multiply a number by 6 and subtracting 6 gives the same result as multiplying the number by 3 and subtracting 4. Find the number The phrase [I]a number [/I]means an arbitrary variable, let's call it x. multiply a number by 6 and subtract 6: 6x - 6 Multiply a number by 3 and subtract 4: 3x - 4 The phrase [I]gives the same result[/I] means an equation. So we set 6x - 6 equal to 3x - 4 6x - 6 = 3x - 4 To solve this equation for x, we type it in our search engine and we get: x = [B]2/3[/B]
Multiplying a number by 6 is equal to the number increased by 9
Multiplying a number by 6 is equal to the number increased by 9. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. Multiply it by 6 --> 6x We set this equal to the same number increased by 9. Increased by means we add: [B]6x = x + 9 <-- This is our algebraic expression [/B] To solve this equation, we [URL='https://www.mathcelebrity.com/1unk.php?num=6x%3Dx%2B9&pl=Solve']type it into the search engine [/URL]and get x = 1.8.
My brother is x years old. I am 5 years older than him. Our combined age is 30 years old. How old is
My brother is x years old. I am 5 years older than him. Our combined age is 30 years old. How old is my brother Brother's age is x: I am 5 years older, meaning I'm x + 5: The combined age is found by adding: x + (x + 5) = 30 Group like terms: 2x + 5 = 30 To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D30&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]12.5[/B]
n = b + d^2a for a
n = b + d^2a for a Let's start by isolating the one term with the a variable. Subtract b from each side: n - b = b - b + d^2a Cancel the b terms on the right side and we get: n - b = d^2a With the a term isolated, let's divide each side of the equation by d^2: (n - b)/d^2 = d^2a/d^2 Cancel the d^2 on the right side, and we'll display this with the variable to solve on the left side: a = [B](n - b)/d^2 [MEDIA=youtube]BCEVsZmoKoQ[/MEDIA][/B]
n and m are congruent and supplementary. prove n and m are right angles
n and m are congruent and supplementary. prove n and m are right angles Given: [LIST] [*]n and m are congruent [*]n and m are supplementary [/LIST] If n and m are supplementary, that means we have the equation: m + n = 180 We're also given n and m are congruent, meaning they are equal. So we can substitute n = m into the supplementary equation: m + m = 180 To solve this equation for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm%3D180&pl=Solve']we type it in our search engine[/URL] and we get: m = 90 This means m = 90, n = 90, which means they are both right angles since by definition, a right angle is 90 degrees.
n times 146, reduced by 94 is the same as h
n times 146, reduced by 94 is the same as h n time 146 146n Reduced by 94 146n - 94 Is the same as h means an equation: [B]146n - 94 = h[/B]
n=i*x+y for i
n=i*x+y for i This is a literal equation. Subtract y from each side of the equation: n - y = i*x + y - y The y's cancel on the right side, so we have: n - y = ix Divide each side of the equation by x, to isolate i (n - y)/x = ix/x The x's cancel on the right side, so we have: i = [B](n - y)/x[/B]
Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daug
Nancy is 10 years less than 3 times her daughters age. If Nancy is 41 years old, how old is her daughter? Declare variables for each age: [LIST] [*]Let Nancy's age be n [*]Let her daughter's age be d [/LIST] We're given two equations: [LIST=1] [*]n = 3d - 10 [*]n = 41 [/LIST] We set 3d - 10 = 41 and solve for d: Solve for [I]d[/I] in the equation 3d - 10 = 41 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants -10 and 41. To do that, we add 10 to both sides 3d - 10 + 10 = 41 + 10 [SIZE=5][B]Step 2: Cancel 10 on the left side:[/B][/SIZE] 3d = 51 [SIZE=5][B]Step 3: Divide each side of the equation by 3[/B][/SIZE] 3d/3 = 51/3 d = [B]17[/B]
Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and i
Nancy started the year with $435 in the bank and is saving $25 a week. Shane started with $875 and is spending $15 a week. [I]When will they both have the same amount of money in the bank?[/I] [I][/I] Set up the Account equation A(w) where w is the number of weeks that pass. Nancy (we add since savings means she accumulates [B]more[/B]): A(w) = 25w + 435 Shane (we subtract since spending means he loses [B]more[/B]): A(w) = 875 - 15w Set both A(w) equations equal to each other to since we want to see what w is when the account are equal: 25w + 435 = 875 - 15w [URL='https://www.mathcelebrity.com/1unk.php?num=25w%2B435%3D875-15w&pl=Solve']Type this equation into our search engine to solve for w[/URL] and we get: w =[B] 11[/B]
Nava is 17 years older than Edward. the sum of Navas age and Edwards ages id 29. How old is Nava?
Nava is 17 years older than Edward. the sum of Navas age and Edwards ages id 29. How old is Nava? Let Nava's age be n and Edward's age be e. We have 2 equations: [LIST=1] [*]n = e + 17 [*]n + e = 29 [/LIST] Substitute (1) into (2) (e + 17) + e = 29 Group like terms: 2e + 17 = 29 Running this equation [URL='http://www.mathcelebrity.com/1unk.php?num=2e%2B17%3D29&pl=Solve']through our search engine[/URL], we get: e = 6 Substitute this into equation (1) n = 6 + 17 [B]n = 23[/B]
Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that show
Nick is given $50 to spend on a vacation . He decides to spend $5 a day. Write an equation that shows how much money Nick has after x amount of days. Set up the function M(x) where M(x) is the amount of money after x days. Since spending means a decrease, we subtract to get: [B]M(x) = 50 - 5x[/B]
Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 comple
Nick said that his sister is 4 times as old as his brother, and together their ages add to 20 complete this equation to find his brothers age Let b be the brother's age and s be the sister's age. We're given two equations: [LIST=1] [*]s =4b [*]b + s = 20 [/LIST] Plug (1) into (2): b + 4b = 20 [URL='https://www.mathcelebrity.com/1unk.php?num=b%2B4b%3D20&pl=Solve']Type this equation into the search engine[/URL], and we get: [B]b = 4[/B]
Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years?
Nicole is half as old as Donald. The sum of their ages is 72. How old is Nicole in years? Let n be Nicole's age. Let d be Donald's age. We're given two equations: [LIST=1] [*]n = 0.5d [*]n + d = 72 [/LIST] Substitute equation (1) into (2): 0.5d + d = 72 1.5d = 72 [URL='https://www.mathcelebrity.com/1unk.php?num=1.5d%3D72&pl=Solve']Typing this equation into the search engine and solving for d[/URL], we get: d = [B]48[/B]
Number of cents in q quarters is 275
Number of cents in q quarters is 275 Each quarter makes 25 cents. We write this as 0.25q. Now set this equal to 275 0.25q = 275 Typing this [URL='http://www.mathcelebrity.com/1unk.php?num=0.25q%3D275&pl=Solve']equation in the search engine[/URL], we get [B]q = 1,100[/B].
numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the de
numerator of a fraction is 5 less than its denominator. if 1 is added to the numerator and to the denominator the new fraction is 2/3. find the fraction. Let n be the numerator. Let d be the denominator. We're given 2 equations: [LIST=1] [*]n = d - 5 [*](n + 1)/(d + 1) = 2/3 [/LIST] Substitute equation (1) into equation (2) for n: (d - 5 + 1) / (d + 1) = 2/3 (d - 4) / (d + 1) = 2/3 Cross multiply: 3(d - 4) = 2(d + 1) To solve this equation for d, we type it in our search engine and we get: d = 14 Substitute d = 14 into equation (1) to solve for n: n = 14 - 5 n = 9 Therefore, our fraction n/d is: [B]9/14[/B]
Oceanside Bike Rental Shop charges $15.00 plus $9.00 per hour for renting a bike. Dan paid $51.00 to
Oceanside Bike Rental Shop charges $15.00 plus $9.00 per hour for renting a bike. Dan paid $51.00 to rent a bike. How many hours was he hiking for? Set up the cost equation C(h) where h is the number of hours needed to rent the bike: C(h) = Cost per hour * h + rental charge Using our given numbers in the problem, we have: C(h) = 9h + 15 The problem asks for h, when C(h) = 51. 9h + 15 = 51 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=9h%2B15%3D51&pl=Solve']plug this equation into our search engine[/URL] and we get: h = [B]4[/B]
Oceanside Bike Rental Shop charges 16 dollars plus 6 dollars an hour for renting a bike. Mary paid 5
Oceanside Bike Rental Shop charges 16 dollars plus 6 dollars an hour for renting a bike. Mary paid 58 dollars to rent a bike. How many hours did she pay to have the bike checked out ? Set up the cost function C(h) where h is the number of hours you rent the bike: C(h) = Hourly rental cost * h + initial rental charge C(h) = 6h + 16 Now the problem asks for h when C(h) = 58, so we set C(h) = 58: 6h + 16 = 58 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=6h%2B16%3D58&pl=Solve']type it in our math engine[/URL] and we get: h = [B]7 hours[/B]
Oliver earns $50 per day plus $7.50 for each package he delivers. If his paycheck for the first day
Oliver earns $50 per day plus $7.50 for each package he delivers. If his paycheck for the first day was $140, how many packages did he deliver that day? His total earnings per day are the Flat Fee of $50 plus $7.50 per package delivered. We have: 50 + 7.50p = 140 where p = the number of packages delivered Using our [URL='http://www.mathcelebrity.com/1unk.php?num=50%2B7.50p%3D140&pl=Solve']equation solver[/URL], we have: [B]p = 12[/B]
Omar mows lawns for $9.25 per hour. He spends $7.50 on gas for the mower. How much does he make if h
Omar mows lawns for $9.25 per hour. He spends $7.50 on gas for the mower. How much does he make if he works h hours? We have the following profit equation: Profit = Revenue - Cost: Revenue = Hourly rate * number of hours [B]9.25h - 7.50[/B]
On a Math test, 12 students earned an A. This number is exactly 25% of the total number of students
On a Math test, 12 students earned an A. This number is exactly 25% of the total number of students in the class. How many students are in the class? Let the total number of students be s. Since 25% is 0.25 as a decimal, We have an equation: 0.25s = 12 [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%3D12&pl=Solve']Type this equation into our search engine[/URL], and we get: s = [B]48[/B]
On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two
On an algebra test, the highest grade was 42 points higher than the lowest grade. The sum of the two grades was 138. Find the lowest grade. [U]Let h be the highest grade and l be the lowest grade. Set up the given equations:[/U] (1) h = l + 42 (2) h + l = 138 [U]Substitute (1) into (2)[/U] l + 42 + l = 138 [U]Combine l terms[/U] 2l + 42 = 138 [U]Enter that equation into our [URL='http://www.mathcelebrity.com/1unk.php?num=2l%2B42%3D138&pl=Solve']equation calculator[/URL] to get[/U] [B]l = 48 [/B] [U]Substitute l = 48 into (1)[/U] h = 48 + 42 [B]h = 90[/B]
On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday
On Monday the office staff at your school paid 8.77 for 4 cups of coffee and 7 bagels. On Wednesday they paid 15.80 for 8 cups of coffee and 14 bagels. Can you determine the cost of a bagel Let the number of cups of coffee be c Let the number of bagels be b. Since cost = Price * Quantity, we're given two equations: [LIST=1] [*]7b + 4c = 8.77 [*]14b + 8c = 15.80 [/LIST] We have a system of equations. We can solve this 3 ways: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=7b+%2B+4c+%3D+8.77&term2=14b+%2B+8c+%3D+15.80&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we use, we get the same answer [LIST] [*]The system is inconsistent. Therefore, we have no answer. [/LIST]
On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a
On the first day of ticket sales the school sold 3 senior citizen tickets and 10 child tickets for a total of $82. The school took in $67 on the second day by selling 8 senior citizen tickets And 5 child tickets. What is the price of each ticket? Let the number of child tickets be c Let the number of senior citizen tickets be s We're given two equations: [LIST=1] [*]10c + 3s = 82 [*]5c + 8s = 67 [/LIST] We have a system of simultaneous equations. We can solve it using any one of 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10c+%2B+3s+%3D+82&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [LIST] [*][B]c = 7[/B] [*][B]s = 4[/B] [/LIST]
One number exceeds another by 15. The sum of the numbers is 51. What are these numbers
One number exceeds another by 15. The sum of the numbers is 51. What are these numbers? Let the first number be x, and the second number be y. We're given two equations: [LIST=1] [*]x = y + 15 [*]x + y = 51 [/LIST] Plug (1) into (2) (y + 15) + y = 51 Combine like terms: 2y + 15 = 51 [URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B15%3D51&pl=Solve']Plug this equation into the search engine[/URL] and we get: [B]y = 18[/B] Now plug this into (1) to get: x = 18 + 15 [B]x = 33[/B]
One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a c
One number is 1/4 of another number. The sum of the two numbers is 25. Find the two numbers. Use a comma to separate your answers. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x = 1/4y [*]x + y = 25 [/LIST] Substitute (1) into (2) 1/4y + y = 25 Since 1/4 = 0.25, we have: 0.25y + y = 25 [URL='https://www.mathcelebrity.com/1unk.php?num=0.25y%2By%3D25&pl=Solve']Type this equation into the search engine[/URL] to get: [B]y = 20 [/B] Now, substitute this into (1) to solve for x: x = 1/4y x = 1/4(20) [B]x = 5 [/B] The problem asks us to separate the answers by a comma. So we write this as: [B](x, y) = (5, 20)[/B]
One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers.
One number is 1/5 of another number. The sum of the two numbers is 18. Find the two numbers. Let the two numbers be x and y. We're given: [LIST=1] [*]x = 1/5y [*]x + y = 18 [/LIST] Substitute (1) into (2): 1/5y + y = 18 1/5 = 0.2, so we have: 1.2y = 18 [URL='https://www.mathcelebrity.com/1unk.php?num=1.2y%3D18&pl=Solve']Type 1.2y = 18 into the search engine[/URL], and we get [B]y = 15[/B]. Which means from equation (1) that: x = 15/5 [B]x = 3 [/B] Our final answer is [B](x, y) = (3, 15)[/B]
One number is 3 times another. Their sum is 44.
One number is 3 times another. Their sum is 44. Let the first number be x, and the second number be y. We're given: [LIST=1] [*]x = 3y [*]x + y = 44 [/LIST] Substitute (1) into (2): 3y + y = 44 [URL='https://www.mathcelebrity.com/1unk.php?num=3y%2By%3D44&pl=Solve']Type this equation into the search engine[/URL], and we get: [B]y = 11[/B] Plug this into equation (1): x = 3(11) [B]x = 33[/B]
one number is 3 times as large as another. Their sum is 48. Find the numbers
one number is 3 times as large as another. Their sum is 48. Find the numbers Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x = 3y [*]x + y = 48 [/LIST] Substitute equation (1) into equation (2): 3y + y = 48 To solve for y, [URL='https://www.mathcelebrity.com/1unk.php?num=3y%2By%3D48&pl=Solve']we type this equation into the search engine[/URL] and we get: [B]y = 12[/B] Now, plug y = 12 into equation (1) to solve for x: x = 3(12) [B]x = 36[/B]
One number is 8 times another number. The numbers are both positive and have a difference of 70.
One number is 8 times another number. The numbers are both positive and have a difference of 70. Let the first number be x, the second number be y. We're given: [LIST=1] [*]x = 8y [*]x - y = 70 [/LIST] Substitute(1) into (2) 8y - y = 70 [URL='https://www.mathcelebrity.com/1unk.php?num=8y-y%3D70&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]y = 10[/B] <-- This is the smaller number Plug this into Equation (1), we get: x = 8(10) [B]x = 80 [/B] <-- This is the larger number
One number is equal to the square of another. Find the numbers if both are positive and their sum is
One number is equal to the square of another. Find the numbers if both are positive and their sum is 650 Let the number be n. Then the square is n^2. We're given: n^2 + n = 650 Subtract 650 from each side: n^2 + n - 650 = 0 We have a quadratic equation. [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-650%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']We type this into our search engine[/URL] and we get: n = 25 and n = -26 Since the equation asks for a positive solution, we use [B]n = 25[/B] as our first solution. the second solution is 25^2 = [B]625[/B]
one number is twice a second number. the sum of those numbers is 45
one number is twice a second number. the sum of those numbers is 45. Let the first number be x and the second number be y. We're given: [LIST=1] [*]x = 2y [*]x + y = 45 [/LIST] Substitute Equation (1) into Equation (2): 2y + y = 45 [URL='https://www.mathcelebrity.com/1unk.php?num=2y%2By%3D45&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]y = 15[/B] Plug this into equation (1) to solve for x, and we get: x = 2(15) [B]x = 30[/B]
One positive number is one-fifth of another number. The difference between the two numbers is 192, f
One positive number is one-fifth of another number. The difference between the two numbers is 192, find the numbers. Let the first number be x and the second number be y. We're given two equations: [LIST=1] [*]x = y/5 [*]x + y = 192 [/LIST] Substitute equation 1 into equation 2: y/5 + y = 192 Since 1 equals 5/5, we rewrite our equation like this: y/5 = 5y/5 = 192 We have fractions with like denominators, so we add the numerators: (1 + 5)y/5 = 192 6y/5 = 192 [URL='https://www.mathcelebrity.com/prop.php?num1=6y&num2=192&den1=5&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Type this equation into our search engine[/URL], and we get: [B]y = 160[/B] Substitute this value into equation 1: x = 160/5 x = [B]32[/B]
One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels.
One third of the bagels in a bakery are sesame bagels. There are 72 sesame bagels. Set up our equation where b is the number of total bagels 72 = b/3 Multiply each side by 3 [B]b = 216[/B]
Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each c
Orange Theory is currently offering a deal where you can buy a fitness pass for $100 and then each class is $13, otherwise it is $18 for each class. After how many classes is the total cost with the fitness pass the same as the total cost without the fitness pass? Let the number of classes be c. For the fitness pass plan, we have the total cost of: 13c + 100 For the flat rate plan, we have the total cost of: 18c The question asks for c when both plans are equal. So we set both costs equal and solve for c: 13c + 100 = 18c We [URL='https://www.mathcelebrity.com/1unk.php?num=13c%2B100%3D18c&pl=Solve']type this equation into our math engine[/URL] and we get: c = [B]20[/B]
Oscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his supplies
Oscar makes a large purchase at Home Depot and plans to rent one of its trucks to take his supplies home. The most he wants to spend on the truck is $56.00. If Home Depot charges $17.00 for the first 75 minutes and $5.00 for each additional 15 min, for how long can Oscar keep the truck and remain within his budget? Set up the cost equation C(m) where m is the number of minutes for rental: C(m) = 17 * min(m, 75) + max(0, 5(m - 75)) If Oscar uses the first 75 minutes, he spends $17. So he's left with: $56 - $17 = $38 $38 / $5 = 7 Remainder 3 We remove the remainder 3, since it's not a full 15 minute block. So Oscar can rent the truck for: 7 * 15 minute blocks = [B]105 minutes[/B]
p = i^2r for r
p = i^2r for r Divide each side of the equation by i^2 to isolate r: p/i^2 = i^2/ri^2 Cancel the i^2 on the right side and we get: r = [B]p/i^2[/B]
p/q = f/q- f for f
p/q = f/q- f for f Isolate f in this literal equation. Factor out f on the right side: p/q = f(1/q - 1) Rewriting the term in parentheses, we get: p/q = f(1 - q)/q Cross multiply: f = pq/q(1 - q) Cancelling the q/q on the right side, we get: f = [B]p/(1 - q)[/B]
p/q=f/q-f for f
p/q=f/q-f for f To solve this literal equation for f, let's factor out f on the right side: p/q=f(1/q-1) Divide each side by (1/q - 1) p/(q(1/q - 1)) = f(1/q-1)/(1/q - 1) Cancelling the (1/q - 1) on the right side, we get: f = p/(1/q - 1) Rewriting this since (1/q -1) = (1 - q)/q since q/q = 1 we have: f = [B]pq/(1 - q)[/B]
P/v=nr/t for r
P/v=nr/t for r Cross multiply to solve this literal equation: Pt = nrv Divide each side of the equation by nv: Pt/nv = nrv/nv Cancel the nv's on the right side, we get: r = [B]Pt/nv[/B]
P=15+5d/11 for d
Subtract 15 from each side: 5d/11 = P - 15 Multiply each side by 11 5d = 11p - 165 Divide each side of the equation by d: d = (11p - 165) ------------ 5
Pam has two part-time jobs. At one job, she works as a cashier and makes $8 per hour. At the second
Pam has two part-time jobs. At one job, she works as a cashier and makes $8 per hour. At the second job, she works as a tutor and makes$12 per hour. One week she worked 30 hours and made$268 . How many hours did she spend at each job? Let the cashier hours be c. Let the tutor hours be t. We're given 2 equations: [LIST=1] [*]c + t = 30 [*]8c + 12t = 268 [/LIST] To solve this system of equations, we can use 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+t+%3D+30&term2=8c+%2B+12t+%3D+268&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we use, we get the same answer: [LIST] [*]c = [B]23[/B] [*]t = [B]7[/B] [/LIST]
Penelope and Owen work at a furniture store. Penelope is paid $215 per week plus 3.5% of her total s
Penelope and Owen work at a furniture store. Penelope is paid $215 per week plus 3.5% of her total sales in dollars, xx, which can be represented by g(x)=215+0.035x. Owen is paid $242 per week plus 2.5% of his total sales in dollars, xx, which can be represented by f(x)=242+0.025x. Determine the value of xx, in dollars, that will make their weekly pay the same. Set the pay functions of Owen and Penelope equal to each other: 215+0.035x = 242+0.025x Using our [URL='http://www.mathcelebrity.com/1unk.php?num=215%2B0.035x%3D242%2B0.025x&pl=Solve']equation calculator[/URL], we get: [B]x = 2700[/B]
Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each
Penny bought a new car for $25,000. The value of the car has decreased in value at rate of 3% each year since. Let x = the number of years since 2010 and y = the value of the car. What will the value of the car be in 2020? Write the equation, using the variables above, that represents this situation and solve the problem, showing the calculation you did to get your solution. Round your answer to the nearest whole number. We have the equation y(x): y(x) = 25,000(0.97)^x <-- Since a 3 % decrease is the same as multiplying the starting value by 0.97 The problem asks for y(2020). So x = 2020 - 2010 = 10. y(10) = 25,000(0.97)^10 y(10) = 25,000(0.73742412689) y(10) = [B]18,435.60[/B]
Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width?
Perimeter of a rectangle is 372 yards. If the length is 99 yards, what is the width? The perimeter P of a rectangle with length l and width w is: 2l + 2w = P We're given P = 372 and l = 99, so we have: 2(99) + 2w = 372 2w + 198 = 372 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 198 and 372. To do that, we subtract 198 from both sides 2w + 198 - 198 = 372 - 198 [SIZE=5][B]Step 2: Cancel 198 on the left side:[/B][/SIZE] 2w = 174 [SIZE=5][B]Step 3: Divide each side of the equation by 2[/B][/SIZE] 2w/2 = 174/2 w = [B]87[/B]
Peter has $500 in his savings account. He purchased an iPhone that charged him $75 for his activatio
Peter has $500 in his savings account. He purchased an iPhone that charged him $75 for his activation fee and $40 per month to use the service on the phone. Write an equation that models the number of months he can afford this phone. Let m be the number of months. Our equation is: [B]40m + 75 = 500 [/B] <-- This is the equation [URL='https://www.mathcelebrity.com/1unk.php?num=40m%2B75%3D500&pl=Solve']Type this equation into the search engine[/URL], and we get: m = [B]10.625[/B] Since it's complete months, it would be 10 months.
Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he
Peter is buying office supplies. He is able to buy 3 packages of paper and 4 staplers for $40, or he is able to buy 5 packages of paper and 6 staplers for $62. How much does a package of paper cost? How much does a stapler cost? Let the cost of paper packages be p and the cost of staplers be s. We're given two equations: [LIST=1] [*]3p + 4s = 40 [*]5p + 6s = 62 [/LIST] We have a system of equations. We can solve this three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3p+%2B+4s+%3D+40&term2=5p+%2B+6s+%3D+62&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get the same answer: [LIST] [*][B]p = 4[/B] [*][B]s = 7[/B] [/LIST]
Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equati
Peter was thinking of a number. Peter doubles it and adds 0.8 to get an answer of 31. Form an equation with x from the information. Take this algebraic expression in parts, starting with the unknown number x: [LIST] [*]x [*][I]Double it [/I]means we multiply x by 2: 2x [*]Add 0.8: 2x + 0.8 [*]The phrase [I]to get an answer of[/I] means an equation. So we set 2x + 0.8 equal to 31 [/LIST] Build our final algebraic expression: [B]2x + 0.8 = 31[/B] [B][/B] If you have to solve for x, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B0.8%3D31&pl=Solve']type this equation into our search engine[/URL] and we get: x = 15.1
Peter�s Lawn Mowing Service charges $10 per job and $0.20 per square yard. Peter earns $25 for a job
Peter�s Lawn Mowing Service charges $10 per job and $0.20 per square yard. Peter earns $25 for a job. Let y be the number of square yards. We have the following equation: 0.2y + 10 = 25 To solve for y, we[URL='https://www.mathcelebrity.com/1unk.php?num=0.2y%2B10%3D25&pl=Solve'] type this equation into our search engine [/URL]and we get: y = [B]75[/B]
Plane and Parametric Equations in R3
Given a vector A and a point (x,y,z), this will calculate the following items:
1) Plane Equation passing through (x,y,z) perpendicular to A
2) Parametric Equations of the Line L passing through the point (x,y,z) parallel to A
please solve the fifth word problem
Find what was used: Used Money = Prepaid original cost - Remaining Credit Used Money = 20 - 17.47 Used Money = 2.53 Using (m) as the number of minutes, we have the following cost equation: C(m) = 0.11m C(m) = 2.53, so we have: 0.11m = 2.53 Divide each side by 0.11 [B]m = 23[/B]
please solve the fourth word problem
Let x be the first number, y be the second number, and z be the number. We have the following equations: [LIST=1] [*]x + y + z = 305 [*]x = y - 5 [*]z = 3y [/LIST] Substitute (2) and (3) into (1) (y - 5) + y + (3y) = 305 Combine like terms: 5y - 5 = 305 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=5y-5%3D305&pl=Solve']equation solver[/URL] [B]y = 62 [/B] Substitute y = 62 into (3) z = 3(62) [B]z = 186 [/B] x = (62) - 5 [B]x = 57[/B]
please solve the third word problem
A Web music store offers two versions of a popular song. The size of the standard version is 2.7 megabytes (MB). The size of the high-quality version is 4.7 MB. Yesterday, the high-quality version was downloaded three times as often as the standard version. The total size downloaded for the two versions was 4200 MB. How many downloads of the standard version were there? Let s be the standard version downloads and h be the high quality downloads. We have two equations: [LIST=1] [*]h = 3s [*]2.7s + 4.7h = 4200 [/LIST] Substitute (1) into (2) 2.7s + 4.7(3s) = 4200 2.7s + 14.1s = 4200 Combine like terms: 16.8s = 4200 Divide each side by 16.8 [B]s = 250[/B]
Point and a Line
Enter any line equation and a 2 dimensional point. The calculator will figure out if the point you entered lies on the line equation you entered. If the point does not lie on the line, the distance between the point and line will be calculated.
Polar Conics
Given eccentricity (e), directrix (d), and angle θ, this determines the vertical and horizontal directrix polar equations.
pr=xf/y for r
pr=xf/y for r So for this literal equation, we divide each side of the equation by p to isolate r. pr/p = xf/yp Cancel the p's on the left side and we get: r = [B]xf/yp [MEDIA=youtube]6ekuN4H3mM4[/MEDIA][/B]
Pressure Law
This will solve for any of the 4 items in the Pressure Law equation, also known as Gay-Lussacs Law assuming constant volume
P1 ÷ T1 = P2 ÷ T2
Profit Equation
Using the Profit Equation with inputs (Revenue-Cost-Profit-Tax), this determines the relevant output including gross proft, gross profit margin, net profit, and net profit margin.
Prove 0! = 1
Prove 0! = 1 Let n be a whole number, where n! represents the product of n and all integers below it through 1. The factorial formula for n is: n! = n · (n - 1) * (n - 2) * ... * 3 * 2 * 1 Written in partially expanded form, n! is: n! = n * (n - 1)! [U]Substitute n = 1 into this expression:[/U] n! = n * (n - 1)! 1! = 1 * (1 - 1)! 1! = 1 * (0)! For the expression to be true, 0! [U]must[/U] equal 1. Otherwise, 1! <> 1 which contradicts the equation above
q is equal to 207 subtracted from the quantity 4 times q
q is equal to 207 subtracted from the quantity 4 times q 4 time q 4q 207 subtracted from 4 times q: 4q - 207 Set this equal to q: [B]4q - 207 = q [/B]<-- This is our algebraic expression To solve for q, [URL='https://www.mathcelebrity.com/1unk.php?num=4q-207%3Dq&pl=Solve']type this equation into the search engine[/URL]. We get: [B]q = 69[/B]
q=c+d/5 for d
q=c+d/5 for d Subtract c from each side to solve this literal equation: q - c = c - c + d/5 Cancel the c's on the right side, we get d/5 = q - c Multiply each side by 5: 5d/5 = 5(q - c) Cancel the 5's on the left side, we get: [B]d = 5(q - c)[/B]
Quadratic Equations and Inequalities
Solves for quadratic equations in the form ax2 + bx + c = 0. Also generates practice problems as well as hints for each problem.
* Solve using the quadratic formula and the discriminant Δ
* Complete the Square for the Quadratic
* Factor the Quadratic
* Y-Intercept
* Vertex (h,k) of the parabola formed by the quadratic where h is the Axis of Symmetry as well as the vertex form of the equation a(h - h)2 + k
* Concavity of the parabola formed by the quadratic
* Using the Rational Root Theorem (Rational Zero Theorem), the calculator will determine potential roots which can then be tested against the synthetic calculator.
Quartic Equations
Solves quartic equations in the form ax4 + bx3 + cx2 + dx + e using the following methods:
1) Solve the long way for all roots and the discriminant Δ
2) Rational Root Theorem (Rational Zero Theorem) to solve for real roots followed by the synthetic div/quadratic method for the other imaginary roots if applicable.
r less than 164 is 248 more than the product of 216 and r
r less than 164 is 248 more than the product of 216 and r [U]r less than 164:[/U] 164 - r [U]The product of 216 and r:[/U] 216r [U]248 more than the product of 216 and r[/U] 216r + 248 [I]The word is means an equation, so we set 164 - r equal to 216r + 248[/I] [B]164 - r = 216r + 248[/B]
r=l^2w/2 for w
r=l^2w/2 for w Solve this literal equation by isolating w. Cross multiply: 2r = l^2w Divide each side by l^2 w = [B]2r/l^2[/B]
Rachel buys some scarves that cost $10 each and 2 purses that cost $16 each. The cost of Rachel's to
Rachel buys some scarves that cost $10 each and 2 purses that cost $16 each. The cost of Rachel's total purchase is $62. What equation can be used to find n, the number of scarves that Rebecca buys Scarves Cost + Purses Cost = Total Cost [U]Calculate Scarves Cost[/U] Scarves cost = Cost per scarf * number of scarves Scarves cost = 10n [U]Calculate Purses Cost[/U] Purses cost = Cost per purse * number of purses Purses cost = 16 * 2 Purses cost = 32 Total Cost = 62. Plug in our numbers and values to the Total Cost equation : 10n + 32 = 62 Solve for [I]n[/I] in the equation 10n + 32 = 62 [SIZE=5][B]Step 1: Group constants:[/B][/SIZE] We need to group our constants 32 and 62. To do that, we subtract 32 from both sides 10n + 32 - 32 = 62 - 32 [SIZE=5][B]Step 2: Cancel 32 on the left side:[/B][/SIZE] 10n = 30 [SIZE=5][B]Step 3: Divide each side of the equation by 10[/B][/SIZE] 10n/10 = 30/10 n = [B]3[/B]
Rachel runs 2 miles during each track practice. Write an equation that shows the relationship betwe
Rachel runs 2 miles during each track practice. Write an equation that shows the relationship between the practices p and the distance d. Distance equals rate * practicdes, so we have: [B]d = 2p[/B]
Rachel saved $200 and spends $25 each week. Roy just started saving $15 per week. At what week will
Rachel saved $200 and spends $25 each week. Roy just started saving $15 per week. At what week will they have the same amount? Let Rachel's account value R(w) where w is the number of weeks be: R(w) = 200 - 25w <-- We subtract -25w because she spends it every week, decreasing her balance. Let Roy's account value R(w) where w is the number of weeks be: R(w) = 15w Set them equal to each other: 200 - 25w = 15w To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=200-25w%3D15w&pl=Solve']we type it into our search engine[/URL] and get: [B]w = 5[/B]
Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wedne
Rachel works at a bookstore. On Tuesday, she sold twice as many books as she did on Monday. On Wednesday, she sold 6 fewer books than she did on Tuesday. During the 3 days Rachel sold 19 books. Create an equation that can be used to find m, a number of books Rachel sold on Monday. Let me be the number of books Rachel sold on Monday. We're given Tuesday's book sales (t) and Wednesday's books sales (w) as: [LIST=1] [*]t = 2m [*]w = t - 6 [*]m + t + w = 19 [/LIST] Plug (1) and (2) into (3): Since t = 2m and w = t - 6 --> 2m - 6, we have: m + 2m + 2m - 6 = 19 Combine like terms: 5m - 6 = 19 [URL='https://www.mathcelebrity.com/1unk.php?num=5m-6%3D19&pl=Solve']Plugging this equation into our search engine[/URL], we get: [B]m = 5[/B]
Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every c
Rafael is a software salesman. His base salary is $1900 , and he makes an additional $40 for every copy of Math is Fun he sells. Let p represent his total pay (in dollars), and let c represent the number of copies of Math is Fun he sells. Write an equation relating to . Then use this equation to find his total pay if he sells 22 copies of Math is Fun. We want a sales function p where c is the number of copies of Math is Fun p = Price per sale * c + Base Salary [B]p = 40c + 1900 [/B] Now, we want to know Total pay if c = 22 p = 40(22) + 1900 p = 880 + 1900 p = [B]2780[/B]
Rearrange the following equation to make x the subject, and select the correct rearrangement from th
Rearrange the following equation to make x the subject, and select the correct rearrangement from the list below 3x + 2y 1 -------- = --- 4x + y 3 [LIST] [*]x = 7y/13 [*]x = 7y/5 [*]x = -7y [*]x = -3y [*]x = 3y/5 [*]x = -5y/13 [*]x = -y [/LIST] Cross multiply: 3(3x - 2y) = 4x + y Multiply the left side through 9x - 6y = 4x + y Subtract 4x from each side and add 6y to each side 5x = 7y Divide each side by 5 to isolate x, the subject of an equation is the variable to the left [B]x = 7y/5[/B]
Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico?
Rico was born 6 years after Nico. The sum of their age is 36. How old is Nico? Let Rico's age be r Let Nico's age be n We're given two equations: [LIST=1] [*]r = n + 6 [*]n + r = 36 [/LIST] We plug equation (1) into equation (2) for r: n + n + 6 = 36 To solve this equation for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=n%2Bn%2B6%3D36&pl=Solve']type it in our search engine[/URL] and we get: [B]n = 15[/B]
Rigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more poi
Rigby and Eleanor's combined score on the systems of equations test was 181. Rigby scored 9 more points than Eleanor. What were Eleanor and Rigby's scores? Let Rigby's score be r Let Eleanor's score be e We're given two equations: [LIST=1] [*]r = e + 9 [*]e + r = 181 [/LIST] Substitute equation (1) into equation (2): e + (e + 9) = 181 Group like terms: 2e + 9 = 181 To solve this equation for e, we [URL='https://www.mathcelebrity.com/1unk.php?num=2e%2B9%3D181&pl=Solve']type it in our search engine[/URL] and we get: e = [B]86[/B]
Riley is trying to raise money by selling key chains. each key chain costs $2.50. If riley is trying
Riley is trying to raise money by selling key chains. each key chain costs $2.50. If riley is trying to raise $60. How many key chains will he have to sell Let the number of key chains be k. We have the following equation: 2.50k = 60 To solve this equation for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.50k%3D60&pl=Solve']type it in our search engine[/URL] and we get: k = [B]24[/B]
Rob has 40 coins, all dimes and quarters, worth $7.60. How many dimes and how many quarters does he
Rob has 40 coins, all dimes and quarters, worth $7.60. How many dimes and how many quarters does he have? We have two equations where d is the number of dimes and q is the number of quarters: [LIST=1] [*]d + q = 40 [*]0.1d + 0.25q = 7.60 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=d+%2B+q+%3D+40&term2=0.1d+%2B+0.25q+%3D+7.60&pl=Cramers+Method']simultaneous equation calculator[/URL], we get: [B]d = 16 q = 24[/B]
Robert and Robert go to the movie theater and purchase refreshments for their friends. Robert spend
Robert and Robert go to the movie theater and purchase refreshments for their friends. Robert spends a total of $65.25 on 4 drinks and 9 bags of popcorn. Robert spends a total of $51.75 on 8 drinks and 3 bags of popcorn. Write a system of equations that can be used to find the price of one drink and the price of one bag of popcorn. Using these equations, determine and state the price of a bag of popcorn, to the nearest cent. Let d be the cost of each drink, and p be the price of each popcorn bag. We have 2 equations for our system of equations: [LIST=1] [*][B]4d + 9p = 65.25[/B] [*][B]8d + 3p = 51.75[/B] [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+9p+%3D+65.25&term2=8d+%2B+3p+%3D+51.75&pl=Cramers+Method']system of equations calculator[/URL], we get: [LIST] [*]d = 4.5 [*][B]p = 5.25 <-- Since the problem asks for the cost of each popcorn bag[/B] [/LIST]
Robert has 45 dollars. He buys 6 tshirts and has 7 dollars left over. How much did each tshirt cost?
Let x be the price of one t-shirt. Set up an equation: 6 times the number of t-shirts plus 7 dollars left over get him to a total of 45 6x = 45 - 7 6x = 38 Divide each side by 6 [B]x = 6.33[/B]
Sadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they score
Sadie and Connor both play soccer. Connor scored 2 times as many goals as Sadie. Together they scored 9 goals. Could Sadie have scored 4 goals? Why or why not? [U]Assumptions:[/U] [LIST] [*]Let Connor's goals be c [*]Let Sadie's goals be s [/LIST] We're given the following simultaneous equations: [LIST=1] [*]c = 2s [*]c + s = 9 [/LIST] We substitute equation (1) into equation (2) for c: 2s + s = 9 To solve the equation for s, we type it in our search equation and we get: s = [B]3[/B] So [U][B]no[/B][/U], Sadie could not have scored 4 goals since s = 3
sales 45,000 commission rate is 3.6% and salary is $275
sales 45,000 commission rate is 3.6% and salary is $275 Set up the commission function C(s) where s is the salary: C(s) = Commission * s + salary We're given: C(s) = 45,000, commission = 3.6%, which is 0.036 and salary = 275, so we have: 0.036s + 275 = 45000 To solve for s, we type this equation into our search engine and we get: s = [B]1,242,361.11[/B]
Sally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They each
Sally and Adam works a different job. Sally makes $5 per hour and Adam makes $4 per hour. They each earn the same amount per week but Adam works 2 more hours. How many hours a week does Adam work? [LIST] [*]Let [I]s[/I] be the number of hours Sally works every week. [*]Let [I]a[/I] be the number of hours Adam works every week. [*]We are given: a = s + 2 [/LIST] Sally's weekly earnings: 5s Adam's weekly earnings: 4a Since they both earn the same amount each week, we set Sally's earnings equal to Adam's earnings: 5s = 4a But remember, we're given a = s + 2, so we substitute this into Adam's earnings: 5s = 4(s + 2) Multiply through on the right side: 5s = 4s + 8 <-- [URL='https://www.mathcelebrity.com/expand.php?term1=4%28s%2B2%29&pl=Expand']multiplying 4(s + 2)[/URL] [URL='https://www.mathcelebrity.com/1unk.php?num=5s%3D4s%2B8&pl=Solve']Typing this equation into the search engine[/URL], we get s = 8. The problem asks for Adam's earnings (a). We plug s = 8 into Adam's weekly hours: a = s + 2 a = 8 + 2 [B]a = 10[/B]
Sally earns $19.25 per hour. This week she earned $616. Write a two step equation to represent the p
Sally earns $19.25 per hour. This week she earned $616. Write a two step equation to represent the problem Let hours be h. We're given: [B]19.25h = 616[/B]
Sally found 73 seashells on the beach, she gave Mary some of her seashells. She has 10 left. How man
Sally found 73 seashells on the beach, she gave Mary some of her seashells. She has 10 left. How many did she give to Mary? Let the number of seashells Sally gave away as g. We're given: 73 - g = 10 To solve this equation for g, we [URL='https://www.mathcelebrity.com/1unk.php?num=73-g%3D10&pl=Solve']type it in our search engine[/URL] and we get: g = [B]63[/B]
Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64.
Sally is 4 years older than Mark. Twice Sally's age plus 5 times Mark's age is equal to 64. Let Sally's age be s. Let Mark's age be m. We're given two equations: [LIST=1] [*]s = m + 4 [*]2s + 5m = 64 <-- [I]Since Twice means we multiply by 2[/I] [/LIST] Substitute equation (1) into equation (2): 2(m + 4) + 5m = 64 Multiply through: 2m + 8 + 5m = 64 Group like terms: (2 + 5)m + 8 = 64 7m + 8 = 64 [URL='https://www.mathcelebrity.com/1unk.php?num=7m%2B8%3D64&pl=Solve']Type this equation into the search engine[/URL] and we get: m = [B]8[/B]
Salma purchased a prepaid phone card for 30. Long distance calls cost 9 cents a minute using this ca
Salma purchased a prepaid phone card for 30. Long distance calls cost 9 cents a minute using this card. Salma used her card only once to make a long distance call. If the remaining credit on her card is 28.38, how many minutes did her call last? [U]Set up the equation where m is the number of minutes used:[/U] 0.09m = 30 - 28.38 0.09m = 1.62 [U]Divide each side by 0.09[/U] [B]m = 18[/B]
Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which
Sam and Jeremy have ages that are consecutive odd integers. The product of their ages is 783. Which equation could be used to find Jeremy's age, j, if he is the younger man. Let Sam's age be s. Let' Jeremy's age be j. We're given: [LIST=1] [*]s = j + 2 <-- consecutive odd integers [*]sj = 783 [/LIST] Substitute (1) into (2): (j + 2)j = 783 j^2 + 2j = 783 Subtract 783 from each side: j^2 + 2j - 783 = 0 <-- This is the equation to find Jeremy's age. To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=j%5E2%2B2j-783%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']we type this quadratic equation into the search engine[/URL] and get: j = 27, j = -29. Since ages cannot be negative, we have: [B]j = 27[/B]
Sam has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how
Sam has $2.25 in quarters and dimes, and the total number of coins is 12. How many quarters and how many dimes? Let d be the number of dimes. Let q be the number of quarters. We're given two equations: [LIST=1] [*]0.1d + 0.25q = 2.25 [*]d + q = 12 [/LIST] We have a simultaneous system of equations. We can solve this 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=0.1d+%2B+0.25q+%3D+2.25&term2=d+%2B+q+%3D+12&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]d = 5[/B] [*][B]q = 7[/B] [/LIST]
Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John
Sam is 52 years old. This is 20 years less than 3 times the age of John. How old is John Let John's age be j. We're given the following equation: 3j - 20 = 52 ([I]Less than[/I] means we subtract) To solve for j, we [URL='https://www.mathcelebrity.com/1unk.php?num=3j-20%3D52&pl=Solve']type this equation into our search engine[/URL] and we get: j = [B]24[/B]
Sam needs to save $300 to buy a video game system. He is able to save $20 per week. How many weeks w
Sam needs to save $300 to buy a video game system. He is able to save $20 per week. How many weeks will it take till he can buy the video game system? Let w be the number of weeks. We have the following equation: 20w = 300 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=20w%3D300&pl=Solve']equation solver[/URL], we get: [B]w = 15[/B]
Sam purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c
Sam purchased n notebooks. They were 4 dollars each. Write an equation to represent the total cost c that Sam paid. Cost Function is: [B]c = 4n[/B] Or, using n as a function variable, we write: c(n) = 4n
Sam's plumbing service charges a $50 diagnostic fee and then $20 per hour. How much money does he ea
Sam's plumbing service charges a $50 diagnostic fee and then $20 per hour. How much money does he earn, m, when he shows up to your house to do a job that takes h hours [U]Set up the cost equation:[/U] m = Hourly Rate * h + service charge [U]Plugging in our numbers, we get:[/U] [B]m = 20h + 50[/B]
Sara opened an account with $800 and withdrew $20 per week. Jordan opened an account with $500 and d
Sara opened an account with $800 and withdrew $20 per week. Jordan opened an account with $500 and deposited $30 per week. In how many weeks will their account be equal? Each week, Sara's account value is: 800 - 20w <-- Subtract because Sara withdraws money each week Each week, Jordan's account value is: 500 + 30w <-- Add because Jordan deposits money each week Set them equal to each other: 800 - 20w = 500 + 30w Using our [URL='http://www.mathcelebrity.com/1unk.php?num=800-20w%3D500%2B30w&pl=Solve']equation solver[/URL], we get w = 6. Check our work: 800 - 20(6) 800 - 120 680 500 + 30(6) 500 + 180 680
Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money fro
Sarah has $250 in her account. She withdraws $25 per week. How many weeks can she withdraw money from her account and still have money left? Let w be the number of weeks. We have the following equation for the Balance after w weeks: B(w) = 250 - 25w [I]we subtract for withdrawals[/I] The ability to withdrawal money means have a positive or zero balance after withdrawal. So we set up the inequality below: 250 - 25w >= 0 To solve this inequality for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=250-25w%3E%3D0&pl=Solve']type it in our search engine[/URL] and we get: w <= [B]10 So Sarah can withdrawal for up to 10 weeks[/B]
Sarah sells cookies. She has a base month salary of $500 and makes $50 for every cookie she sells. w
Sarah sells cookies. She has a base month salary of $500 and makes $50 for every cookie she sells. whats is the equation. Let S(c) be the equation for the money Sarah makes selling (c) cookies. We have: S(c) = Cost per cookies * c cookies + Base Salary [B]S(c) = 50c + 500[/B]
Sarah starts with $300 in her savings account. She babysits and earns $30 a week to add to her accou
Sarah starts with $300 in her savings account. She babysits and earns $30 a week to add to her account. Write a linear equation to model this situation? Enter your answer in y=mx b form with no spaces. Let x be the number of hours Sarah baby sits. Then her account value y is: y = [B]30x + 300[/B]
Savannah is a salesperson who sells computers at an electronics store. She makes a base pay of $90 e
Savannah is a salesperson who sells computers at an electronics store. She makes a base pay of $90 each day and is also paid a commission for each sale she makes. One day, Savannah sold 4 computers and was paid a total of $100. Write an equation for the function P(x), representing Savannah's total pay on a day on which she sells x computers. If base pay is $90 per day, then the total commission Savannah made for selling 4 computers is: Commission = Total Pay - Base Pay Commission = 100 - 90 Commission = $10 Assuming the commission for each computer is equal, we need to find the commission per computer: Commission per computer = Total Commission / Number of Computers Sold Commission per computer = 10/4 Commission per computer = $2.50 Now, we build the Total pay function P(x): Total Pay = Base Pay + Commission * Number of Computers sold [B]P(x) = 90 + 2.5x[/B]
Sectoral Balance
Solves for any of the 6 inputs in the Sectoral Balance equation by Wynne Godley
Security Market Line and Treynor Ratio
Solves for any of the 4 items in the Security Market Line equation, Risk free rate, market return, Î’, and expected return as well as calculate the Treynor Ratio.
Seven less than 1/4 of a number is 9.
Seven less than 1/4 of a number is 9. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 1/4 of a number means we multiply x by 1/4: x/4 Seven less than this means we subtract 7 from x/4: x/4 - 7 The word [I]is[/I] means an equation, so we set x/4 - 7 equal to 9: [B]x/4 - 7 = 9[/B]
Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself. How man
Shalini gave 0.4 of her plums to her brother and 20% to her sister. She kept 16 for herself. How many plums did she have first? Let's convert everything to decimals. 20% = 0.2 So Shalini gave 0.4 + 0.2 = 0.6 of the plums away. Which means she has 1 = 0.6 = 0.4 or 40% left over. 40% represents 16 plums So our equation is 0.4p = 16 where p is the number of plums to start with Divide each side by 0.4 [B]p = 40[/B]
Shanice won 97 pieces of gum playing basketball at the county fair. At school she gave four to every
Shanice won 97 pieces of gum playing basketball at the county fair. At school she gave four to every student in her math class. She only has 5 remaining. How many students are in her class? Let the number of students be s. We have a situation described by the following equation: 4s + 5 = 97 <-- We add 5 since it's left over to get to 97 [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B5%3D97&pl=Solve']We type this equation into the search engine[/URL] and we get: s = [B]23[/B]
She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked bot
She earns $20 per hour as a carpenter and $25 per hour as a blacksmith, last week Giselle worked both jobs for a total of 30 hours, and a total of $690. How long did Giselle work as a carpenter and how long did she work as a blacksmith? Assumptions: [LIST] [*]Let b be the number of hours Giselle worked as a blacksmith [*]Let c be the number of hours Giselle worked as a carpenter [/LIST] Givens: [LIST=1] [*]b + c = 30 [*]25b + 20c = 690 [/LIST] Rearrange equation (1) to solve for b by subtracting c from each side: [LIST=1] [*]b = 30 - c [*]25b + 20c = 690 [/LIST] Substitute equation (1) into equation (2) for b 25(30 - c) + 20c = 690 Multiply through: 750 - 25c + 20c = 690 To solve for c, we [URL='https://www.mathcelebrity.com/1unk.php?num=750-25c%2B20c%3D690&pl=Solve']type this equation into our search engine[/URL] and we get: c = [B]12 [/B] Now, we plug in c = 12 into modified equation (1) to solve for b: b = 30 - 12 b = [B]18[/B]
She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.9
She ordered 6 large pizzas. Luckily, she had a coupon for 3 off each pizza. If the bill came to 38.94, what was the price for a large pizza? [U]Determine additional amount the pizzas would have cost without the coupon[/U] 6 pizzas * 3 per pizza = 18 [U]Add 18 to our discount price of 38.94[/U] Full price for 6 large pizzas = 38.94 + 18 Full price for 6 large pizzas = 56.94 Let x = full price per pizza before the discount. Set up our equation: 6x = 56.94 Divide each side by 6 [B]x = $9.49[/B]
Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry?
Sherry is 31 years younger than her mom. The sum of their ages is 61. How old is Sherry? Let Sherry's age be s. Let the mom's age be m. We're given two equations: [LIST=1] [*]s = m - 31 [*]m + s = 61 [/LIST] Substitute equation (1) into equation (2) for s: m + m - 31 = 61 To solve for m, [URL='https://www.mathcelebrity.com/1unk.php?num=m%2Bm-31%3D61&pl=Solve']we type this equation into our search engine[/URL] and we get: m = 46 Now, we plug m = 46 into equation (1) to find Sherry's age s: s = 46 - 31 s = [B]15[/B]
Sierra borrows $310 from her brother to buy a lawn mower. She will repay $85 to start, and then anot
Sierra borrows $310 from her brother to buy a lawn mower. She will repay $85 to start, and then another $25 per week. A. Write an equation that can be used to determine w, the number of weeks it will take for Sierra to repay the entire amount. Let w be the number of weeks. We have the equation: 25w + 85 = 310 [URL='https://www.mathcelebrity.com/1unk.php?num=25w%2B85%3D310&pl=Solve']Type this equation into the search engine[/URL], and we get: w = [B]9[/B]
Simultaneous Equations
Solves a system of simultaneous equations with 2 unknowns using the following 3 methods:
1) Substitution Method (Direct Substitution)
2) Elimination Method
3) Cramers Method or Cramers Rule Pick any 3 of the methods to solve the systems of equations 2 equations 2 unknowns
slope is 0 and whose y-intercept is 9.
slope is 0 and whose y-intercept is 9. The standard line equation is y = mx + b where m is the slope and b is the y-intercept is b. Plugging in our numbers, we get: y = 0x + 9 y = [B]9[/B]
Small pizzas were $3 and large pizzas were $5. To feed the throng, it was necessary to spend $475 fo
Small pizzas were $3 and large pizzas were $5. To feed the throng, it was necessary to spend $475 for 125 pizzas. How many small pizzas were purchased? Let s be the number of small pizzas and l be the number of large pizzas. We have two given equations: [LIST=1] [*]l + s = 125 [*]3s + 5l = 475 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=l+%2B+s+%3D+125&term2=3s+%2B+5l+%3D+475&pl=Cramers+Method']simultaneous equation calculator[/URL], we get [B]s = 75[/B]:
Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 c
Soda cans are sold in a local store for 50 cents each. The factory has $900 in fixed costs plus 25 cents of additional expense for each soda can made. Assuming all soda cans manufactured can be sold, find the break-even point. Calculate the revenue function R(c) where s is the number of sodas sold: R(s) = Sale Price * number of units sold R(s) = 50s Calculate the cost function C(s) where s is the number of sodas sold: C(s) = Variable Cost * s + Fixed Cost C(s) = 0.25s + 900 Our break-even point is found by setting R(s) = C(s): 0.25s + 900 = 50s We [URL='https://www.mathcelebrity.com/1unk.php?num=0.25s%2B900%3D50s&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]18.09[/B]
Solve 11 - 1/2y = 3 + 6x for y
Solve 11 - 1/2y = 3 + 6x for y Subtract 11 from each side so we can isolate the y term: 11 -11 - 1/2y = 3 + 6x - 11 Cancelling the 11's on the left side, we get: -1/2y = 6x - 8 <-- Since 3 - 11 = -8 Multiply both sides of the equation by -2 to remove the -1/2 on the left side: -2(-1/2)y = -2(6x - 8) Simplifying, we get: y = [B]-12x + 16[/B]
Solving word problems with the matrix method?
Hello everyone. I am stuck on a work question that we are required to solve using the matrix (or Gauss-Jordan) method. [CENTER]"A car rental company wants to buy 100 new cars. Compact cars cost $12,000 each, intermediate size cars cost $18,000 each, full size cars cost $24,000 each, and the company has a budget of $1,500,000. If they purchase twice as many compact cars as intermediate sized cars, determine the number of cars of each type that they buy, assuming they spend the entire budget." [/CENTER] I am fairly certain that I could solve this easily, except I cannot figure out the proper three equations that correspond to this question. I someone could help me figure them out, it would be greatly appreciated!
Solving word problems with the matrix method?
Let c be the cost of compact cars, i be the cost of intermediate cards, and f be the cost of full-size cars. We have the following equations: [LIST] [*]c + i + f = 100 [*]12,000c + 18,000i + 24,000 f = 1,500,000 [*]c = 2i [/LIST]
Some History teachers at Richmond High School are purchasing tickets for students and their adult ch
Some History teachers at Richmond High School are purchasing tickets for students and their adult chaperones to go on a field trip to a nearby museum. For her class, Mrs. Yang bought 30 student tickets and 30 adult tickets, which cost a total of $750. Mr. Alexander spent $682, getting 28 student tickets and 27 adult tickets. What is the price for each type of ticket? Let the number of adult tickets be a Let the number of student tickets be s We're given two equations: [LIST=1] [*]30a + 30s = 750 [*]27a + 28s = 682 [/LIST] To solve the simultaneous equations, we can use any of three methods below: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=30a+%2B+30s+%3D+750&term2=27a+%2B+28s+%3D+682&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we use, we get the same answers: [LIST] [*][B]a = 18[/B] [*][B]s = 7[/B] [/LIST]
Sports radio stations numbered 220 in 1996. The number of sports radio stations has since increased
Sports radio stations numbered 220 in 1996. The number of sports radio stations has since increased by approximately 14.3% per year. Write an equation for the number of sports radio stations for t years after 1996. If the trend continues, predict the number of sports radio stations in 2015. Equation - where t is the number of years after 1996: R(t) = 220(1.143)^t We Want R(t) for 2015 t = 2015 - 1996 = 19 R(19) = 220(1.143)^19 R(19) = 220 * 12.672969 [B]R(19) = 2788.05 ~ 2,788[/B]
Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis
Stacy and Travis are rock climbing. Stacys rope is 4 feet shorter than 3 times the length of Travis rope. Stacys rope is 23 feet long. Write and solve an equation to find the length t of Travis rope. Let Stacy's rope be s. Travis's rope be t. We have: s = 3t - 4 s = 23 So [B]3t - 4 = 23 [/B] [URL='http://www.mathcelebrity.com/1unk.php?num=3t-4%3D23&pl=Solve']Paste this equation into our search engine[/URL] to get [B]t = 9[/B].
Stacy sells art prints for $12 each. Her expenses are $2.50 per print, plus $38 for equipment. How m
Stacy sells art prints for $12 each. Her expenses are $2.50 per print, plus $38 for equipment. How many prints must she sell for her revenue to equal her expenses? Let the art prints be p Cost function is 38 + 2p Revenue function is 12p Set cost equal to revenue 12p = 38 + 2p Subtract 2p from each side 10p = 38 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=10p%3D38&pl=Solve']equation calculator[/URL] gives us [B]p = 3.8[/B]
Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with.
Steven has some money. If he spends $9, then he will have 3/5 of the amount he started with. Let the amount Steven started with be s. We're given: s - 9 = 3s/5 Multiply each side through by 5 to eliminate the fraction: 5(s - 9) = 5(3s/5) Cancel the 5's on the right side and we get: 5s - 45 = 3s To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=5s-45%3D3s&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]22.5[/B]
Stock A is worth 4.5. Stock B is worth 8.0. Stock C is worth 10.0. She purchased half as many shares
Stock A is worth 4.5. Stock B is worth 8.0. Stock C is worth 10.0. She purchased half as many shares of B as A and half as many shares of C as B. If her investments are worth 660, how many shares of each stock does she own? Let s be the number of shares in Stock A. We have: [LIST=1] [*]A: 4.5s [*]B: 8s/2 = 4s [*]C: 10s/4 = 2.5s [/LIST] Value equation: 4.5s + 4s + 2.5s = 660 Combining like terms: 11s = 660 Using the [URL='http://www.mathcelebrity.com/1unk.php?num=11s%3D660&pl=Solve']equation calculator[/URL], we get [B]s = 60[/B] for Stock A Stock B shares is equal to 1/2A = [B]30[/B] Stock C shares is equal to 1/2B = [B]15[/B]
Strain
Solves for any of the 3 items in the strain equation: Change in Length, Strain, and Original Length
Students stuff envelopes for extra money. Their initial cost to obtain the information for the job w
Students stuff envelopes for extra money. Their initial cost to obtain the information for the job was $140. Each envelope costs $0.02 and they get paid $0.03per envelope stuffed. Let x represent the number of envelopes stuffed. (a) Express the cost C as a function of x. (b) Express the revenue R as a function of x. (c) Determine analytically the value of x for which revenue equals cost. a) Cost Function [B]C(x) = 140 + 0.02x[/B] b) Revenue Function [B]R(x) = 0.03x[/B] c) Set R(x) = C(x) 140 + 0.02x = 0.03x Using our [URL='http://www.mathcelebrity.com/1unk.php?num=140%2B0.02x%3D0.03x&pl=Solve']equation solver[/URL], we get x = [B]14,000[/B]
Substitute the given values into given formula and solve for the unknown variable. S=4LW + 2 WH; S=
Substitute the given values into given formula and solve for the unknown variable. S = 4LW + 2 WH; S= 144, L= 8, W= 4. H= S = 4LW + 2 WH Substituting our given values, we have: 144 = 4(8)(4) + 2(4)H 144 = 128 + 8H Using our [URL='http://www.mathcelebrity.com/1unk.php?num=128%2B8h%3D144&pl=Solve']equation calculator[/URL], we get: [B]H = 2[/B]
sum of 3 consecutive odd integers equals 1 hundred 17
sum of 3 consecutive odd integers equals 1 hundred 17 The sum of 3 consecutive odd numbers equals 117. What are the 3 odd numbers? 1) Set up an equation where our [I]odd numbers[/I] are n, n + 2, n + 4 2) We increment by 2 for each number since we have [I]odd numbers[/I]. 3) We set this sum of consecutive [I]odd numbers[/I] equal to 117 n + (n + 2) + (n + 4) = 117 [SIZE=5][B]Simplify this equation by grouping variables and constants together:[/B][/SIZE] (n + n + n) + 2 + 4 = 117 3n + 6 = 117 [SIZE=5][B]Subtract 6 from each side to isolate 3n:[/B][/SIZE] 3n + 6 - 6 = 117 - 6 [SIZE=5][B]Cancel the 6 on the left side and we get:[/B][/SIZE] 3n + [S]6[/S] - [S]6[/S] = 117 - 6 3n = 111 [SIZE=5][B]Divide each side of the equation by 3 to isolate n:[/B][/SIZE] 3n/3 = 111/3 [SIZE=5][B]Cancel the 3 on the left side:[/B][/SIZE] [S]3[/S]n/[S]3 [/S]= 111/3 n = 37 Call this n1, so we find our other 2 numbers n2 = n1 + 2 n2 = 37 + 2 n2 = 39 n3 = n2 + 2 n3 = 39 + 2 n3 = 41 [SIZE=5][B]List out the 3 consecutive odd numbers[/B][/SIZE] ([B]37, 39, 41[/B]) 37 ? 1st number, or the Smallest, Minimum, Least Value 39 ? 2nd number 41 ? 3rd or the Largest, Maximum, Highest Value
sum of 5 times h and twice g is equal to 23
sum of 5 times h and twice g is equal to 23 Take this [U]algebraic expressions[/U] problem in pieces. Step 1: 5 times h: 5h Step 2: Twice g means we multiply g by 2: 2g Step 3: sum of 5 times h and twice g means we add 2g to 5h 5h + 2g Step 4: The phrase [I]is equal to[/I] means an equation, so we set 5h + 2g equal to 23: [B]5h + 2g = 23[/B]
sum of a number and 7 is subtracted from 15 the result is 6.
Sum of a number and 7 is subtracted from 15 the result is 6. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We take this expression in pieces. Sum of a number and 7 x + 7 Subtracted from 15 15 - (x + 7) The result is means an equation, so we set this expression above equal to 6 [B]15 - (x + 7) = 6 <-- This is our algebraic expression[/B] If the problem asks you to solve for x, we Group like terms 15 - x - 7 = 6 8 - x = 6 [URL='https://www.mathcelebrity.com/1unk.php?num=8-x%3D6&pl=Solve']Type 8 - x = 6 into the search engine[/URL], and we get [B]x = 2[/B]
Sum of a number and it's reciprocal is 6. What is the number?
Sum of a number and it's reciprocal is 6. What is the number? Let the number be n. The reciprocal is 1/n. The word [I]is[/I] means an equation, so we set n + 1/n equal to 6 n + 1/n = 6 Multiply each side by n to remove the fraction: n^2 + 1 = 6n Subtract 6n from each side: [B]n^2 - 6n + 1 = 0 [/B]<-- This is our algebraic expression If the problem asks you to solve for n, then you [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-6n%2B1%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']type this quadratic equation into our search engine[/URL].
SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how m
SuperFit Gym charges $14 per month, as well as a one-time membership fee of $25 to join. After how many months will I spend a total of $165? [U]Let the number of months be m. We have a total spend T of:[/U] cost per month * m + one-time membership fee = T [U]Plugging in our numbers, we get:[/U] 14m + 25 = 165 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=14m%2B25%3D165&pl=Solve']type it in our search engine[/URL] and we get: m = [B]10[/B]
Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin doe
Suppose Briley has 10 coins in quarters and dimes and has a total of 1.45. How many of each coin does she have? Set up two equations where d is the number of dimes and q is the number of quarters: (1) d + q = 10 (2) 0.1d + 0.25q = 1.45 Rearrange (1) into (3) to solve for d (3) d = 10 - q Now plug (3) into (2) 0.1(10 - q) + 0.25q = 1.45 Multiply through: 1 - 0.1q + 0.25q = 1.45 Combine q terms 0.15q + 1 = 1.45 Subtract 1 from each side 0.15q = 0.45 Divide each side by 0.15 [B]q = 3[/B] Plug our q = 3 value into (3) d = 10 - 3 [B]d = 7[/B]
Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5?
Suppose that h(x) varies directly with x and h(x)=44 when x = 2. What is h(x) when x = 1.5? Direct variation means we set up an equation: h(x) = kx where k is the constant of variation. For h(x) = 44 when x = 2, we have: 2k = 44 [URL='https://www.mathcelebrity.com/1unk.php?num=2k%3D44&pl=Solve']Type this equation into our search engine[/URL], we get: k = 22 The question asks for h(x) when x = 1.5. So we set up our variation equation, knowing that k = 22. kx = h(x) With k = 22 and x = 1.5, we get: 22(1.5) = h(x) h(x) = [B]33[/B]
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in ga
Suppose that the weight (in pounds) of an airplane is a linear function of the amount of fuel (in gallons) in its tank. When carrying 20 gallons of fuel, the airplane weighs 2012 pounds. When carrying 55 gallons of fuel, it weighs 2208 pounds. How much does the airplane weigh if it is carrying 65 gallons of fuel? Linear functions are written in the form of one dependent variable and one independent variable. Using g as the number of gallons and W(g) as the weight, we have: W(g) = gx + c where c is a constant We are given: [LIST] [*]W(20) = 2012 [*]W(55) = 2208 [/LIST] We want to know W(65) Using our givens, we have: W(20) = 20x + c = 2012 W(55) = 55x + c = 2208 Rearranging both equations, we have: c = 2012 - 20x c = 2208 - 55x Set them both equal to each other: 2012 - 20x = 2208 - 55x Add 55x to each side: 35x + 2012 = 2208 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=35x%2B2012%3D2208&pl=Solve']equation solver[/URL], we see that x is 5.6 Plugging x = 5.6 back into the first equation, we get: c = 2012 - 20(5.6) c = 2012 - 112 c = 2900 Now that we have all our pieces, find W(65) W(65) = 65(5.6) + 2900 W(65) = 264 + 2900 W(65) = [B]3264[/B]
Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6.
Suppose x is a natural number. When you divide x by 7 you get a quotient of q and a remainder of 6. When you divide x by 11 you get the same quotient but a remainder of 2. Find x. [U]Use the quotient remainder theorem[/U] A = B * Q + R where 0 ? R < B where R is the remainder when you divide A by B Plugging in our numbers for Equation 1 we have: [LIST] [*]A = x [*]B = 7 [*]Q = q [*]R = 6 [*]x = 7 * q + 6 [/LIST] Plugging in our numbers for Equation 2 we have: [LIST] [*]A = x [*]B = 11 [*]Q = q [*]R = 2 [*]x = 11 * q + 2 [/LIST] Set both x values equal to each other: 7q + 6 = 11q + 2 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=7q%2B6%3D11q%2B2&pl=Solve']equation calculator[/URL], we get: q = 1 Plug q = 1 into the first quotient remainder theorem equation, and we get: x = 7(1) + 6 x = 7 + 6 [B]x = 13[/B] Plug q = 1 into the second quotient remainder theorem equation, and we get: x = 11(1) + 2 x = 11 + 2 [B]x = 13[/B]
Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $16
Suppose you have $28.00 in your bank account and start saving $18.25 every week. Your friend has $161.00 in his account and is withdrawing $15 every week. When will your account balances be the same? Set up savings and withdrawal equations where w is the number of weeks. B(w) is the current balance [LIST] [*]You --> B(w) = 18.25w + 28 [*]Your friend --> B(w) = 161 - 15w [/LIST] Set them equal to each other 18.25w + 28 = 161 - 15w [URL='http://www.mathcelebrity.com/1unk.php?num=18.25w%2B28%3D161-15w&pl=Solve']Type that problem into the search engine[/URL], and you get [B]w = 4[/B].
Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on adverti
Suppose you write a book. The printer charges $4 per book to print it, and you spend 5500 on advertising. You sell the book for $15 a copy. How many copies must you sell to break even. Profit per book is: P = 15 - 4 P = 11 We want to know the number of books (b) such that: 11b = 5500 <-- Breakeven means cost equals revenue [URL='https://www.mathcelebrity.com/1unk.php?num=11b%3D5500&pl=Solve']Typing this equation into the search engine[/URL], we get: b = [B]500[/B]
Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each.
Susan makes and sells purses. The purses cost her $15 each to make, and she sells them for $30 each. This Saturday, she is renting a booth at a craft fair for $50. Write an equation that can be used to find the number of purses Susan must sell to make a profit of $295 Set up the cost function C(p) where p is the number of purses: C(p) = Cost per purse * p + Booth Rental C(p) = 15p + 50 Set up the revenue function R(p) where p is the number of purses: R(p) = Sale price * p R(p) = 30p Set up the profit function which is R(p) - C(p) equal to 295 30p - (15p + 50) = 295 To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30p-%2815p%2B50%29%3D295&pl=Solve']we type it into our search engine[/URL] and we get: p = [B]23[/B]
T-shirts sell for $19.97 and cost $14.02 to produce. Which equation represents p, the profit, in ter
T-shirts sell for $19.97 and cost $14.02 to produce. Which equation represents p, the profit, in terms of x, the number of t-shirts sold? A) p = $19.97x - $14.02 B) p = x($19.97 - $14.02) C) p = $19.97 + $14.02x D) p = x($19.97 + $14.02) [B]B) p = x($19.97 - $14.02)[/B] [B][/B] [LIST] [*]Profit is Revenue - Cost [*]Each shirt x generates a profit of 19.97 - 14.02 [/LIST]
Tamira and her 3 friends spent a total of $37 for a large pizza and 4 sodas. Each soda cost $2. Whic
Tamira and her 3 friends spent a total of $37 for a large pizza and 4 sodas. Each soda cost $2. Which equation can be used to find p, the cost of the pizza? We add the cost of the pizza (p) to the 4 sodas @ $2 each to get 37 p + 4(2) = 37 [B]p + 8 = 37 (This is the equation) [/B] If the problem asks you to solve for p, then we [URL='https://www.mathcelebrity.com/1unk.php?num=p%2B8%3D37&pl=Solve']type the equation above into our search engine[/URL] and we get: p = [B]29[/B]
tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total
tammy earns $18000 salary with 4% comission on sales. How much should she sell to earn $55,000 total We have a commission equation below: Sales * Commission percent = Salary We're given 4% commission percent and 55,000 salary. With 4% as 0.04, we have: Sales * 0.04 = 55,000 Divide each side of the equation by 0.04, and we get: Sales = [B]1,375,000[/B]
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 32
The admission fee at an amusement park is $1.50 for children and $4 for adults. On a certain day, 327 people entered the park , and the admission fee collected totaled 978.00 dollars . How many children and how many adults were admitted? Let the number of children's tickets be c. Let the number of adult tickets be a. We're given two equations: [LIST=1] [*]a + c = 327 [*]4a + 1.50c = 978 [/LIST] We can solve this system of equation 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+c+%3D+327&term2=4a+%2B+1.50c+%3D+978&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answers: [LIST] [*][B]a = 195[/B] [*][B]c = 132[/B] [/LIST]
The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day,
The admission fee at an amusement park is $1.50 for children and $4.00 for adults. On a certain day, 281 people entered the park, and the admission fees collected totaled $784 . How many children and how many adults were admitted? Let c be the number of children and a be the number of adults. We have two equations: [LIST=1] [*]a + c = 281 [*]4a + 1.5c = 784 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=a%2Bc%3D281&term2=4a+%2B+1.5c+%3D+784&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [LIST] [*][B]a = 145[/B] [*][B]c = 136[/B] [/LIST]
The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. Wha
The arithmetic mean (average) of 17, 26, 42, and 59 is equal to the arithmetic mean of 19 and N. What is the value of N ? Average of the first number set is [URL='https://www.mathcelebrity.com/statbasic.php?num1=17%2C26%2C42%2C59&num2=+0.2%2C0.4%2C0.6%2C0.8%2C0.9&pl=Number+Set+Basics']using our average calculator[/URL] is: 36 Now, the mean (average) or 19 and N is found by adding them together an dividing by 2: (19 + N)/2 Since both number sets have equal means, we set (19 + N)/2 equal to 36: (19 + N)/2 = 36 Cross multiply: 19 + N = 36 * 2 19 + n = 72 To solve for n, we [URL='https://www.mathcelebrity.com/1unk.php?num=19%2Bn%3D72&pl=Solve']type this equation into our search engine[/URL] and we get: n = [B]53[/B]
The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the numbe
The average cost of printing a book in a publishing company is c(x) = 5.5x+kx , where x is the number of books printed that day and k is a constant. Find k, if on the day when 200 were printed the average cost was $9 per book. We are given: c(200) = 9, so we have: 9 = 5.5(200) + k(200) 200k + 1100 = 9 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=200k%2B1100%3D9&pl=Solve']equation solver[/URL], we get: [B]k = -5.455[/B]
The average height of a family of 6 is 6 feet. After the demise of the mother, the average height re
The average height of a family of 6 is 6 feet. After the demise of the mother, the average height remained the same. What is the height of the mother? [LIST] [*]Let the height of the family without the mom be f. Let the height of the mother be m. [*]Averages mean we add the heights and divide by the number of people who were measured. [/LIST] We're given two equations: [LIST=1] [*](f + m)/6 = 6 [*]f/5 = 6 [/LIST] Cross multiplying equation (2), we get: f = 5 * 6 f = 30 Plug f = 30 into equation (1), we get: (30 + m)/6 = 6 Cross multiplying, we get: m + 30 = 6 * 6 m + 30 = 36 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B30%3D36&pl=Solve']type it in our search engine[/URL] and we get: m = [B]6[/B] [SIZE=3][FONT=Arial][COLOR=rgb(34, 34, 34)][/COLOR][/FONT][/SIZE]
The average of 16 and x is 21. Find x.
The average of 16 and x is 21. Find x. The average of 2 numbers is the sum of the 2 numbers divided by 2. So we have: (16 + x)/2 = 21 Cross multiply: 16 + x = 21*2 16 + x = 42 To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=16%2Bx%3D42&pl=Solve']we type this expression into the search engine[/URL] and get [B]x = 26[/B]. Check our work by restating our answer: The average of 16 and 26 is 21. TRUE.
the average of eighty-five and a number m is ninety
the average of eighty-five and a number m is ninety Average of 2 numbers means we add both numbers and divide by 2: (85 + m)/2 = 90 Cross multiply: m + 85 = 90 * 2 m + 85 = 180 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=m%2B85%3D180&pl=Solve']type it in our math engine [/URL]and we get: m = [B]95[/B]
The basketball team is selling candy as a fundraiser. A regular candy bar cost 0.75 and a king sized
The basketball team is selling candy as a fundraiser. A regular candy bar cost 0.75 and a king sized candy bar costs 1.50. In the first week of the sales the team made 36.00. Exactly 12 regular sized bars were sold that week. How many king size are left? Let r be the number of regular bars and k be the number of king size bars. Set up our equations: [LIST=1] [*]0.75r + 1.5k = 36 [*]r = 12 [/LIST] [U]Substitute (2) into (1)[/U] 0.75(12) + 1.5k = 36 9 + 1.5k = 36 [U]Use our equation solver, we get:[/U] [B]k = 18[/B]
The bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the lar
The bigger of 2 numbers in 5 larger than the smaller. Twice the smaller, increased by, twice the larger, is equal to 50. Find each number. Let the big number be b. Let the small number be s. We're given two equations: [LIST=1] [*]b = s + 5 [*]2s + 2b = 50 [/LIST] Substitute equation (1) into equation (2) 2s + 2(s + 5) = 50 [URL='https://www.mathcelebrity.com/1unk.php?num=2s%2B2%28s%2B5%29%3D50&pl=Solve']Type this equation into our search engine[/URL], and we get: [B]s = 10[/B] Now substitute s = 10 into equation (1) to solve for b: b = 10 + 5 [B]b = 15[/B]
The bill for the repair of a car was $294. The cost of parts was $129, and labor charge was $15 per
The bill for the repair of a car was $294. The cost of parts was $129, and labor charge was $15 per hour. How many hours did it take to repair the car? Write a sentence as your answer. Let h be the number of hours. We have: 15h + 129 = 294 To solve this equation for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=15h%2B129%3D294&pl=Solve']type it in the search engine [/URL]and we get: h = [B]11[/B]
The bill from your plumber was $134. The cost for labor was $32 per hour. The cost materials was $46
The bill from your plumber was $134. The cost for labor was $32 per hour. The cost materials was $46. How many hours did the plumber work? Set up the cost equation where h is the number of hours worked: 32h + 46 = 134 [URL='https://www.mathcelebrity.com/1unk.php?num=32h%2B46%3D134&pl=Solve']Typing this equation into our search engine[/URL], we get [B]h = 2.75[/B].
The blue star publishing company produces daily "Star news". It costs $1200 per day to operate regar
The blue star publishing company produces daily "Star news". It costs $1200 per day to operate regardless of whether any newspaper are published. It costs 0.20 to publish each newspaper. Each daily newspaper has $850 worth of advertising and each newspaper is sold for $.30. Find the number of newspaper required to be sold each day for the Blue Star company to 'break even'. I.e all costs are covered. Build our cost function where n is the number of newspapers sold: C(n) = 1200+ 0.2n Now build the revenue function: R(n) = 850 + 0.3n Break even is where cost and revenue are equal, so set C(n) = R(n) 1200+ 0.2n = 850 + 0.3n Using our [URL='http://www.mathcelebrity.com/1unk.php?num=1200%2B0.2n%3D850%2B0.3n&pl=Solve']equation solver[/URL], we get: [B]n = 3,500[/B]
The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the
The cost for parking at a parking garage is 2.25 plus an additional 1.50 for each hour. What is the total cost to park for 5 hours? Set up our equation where C is cost and h is the number of hours used to park C = 1.5h + 2.25 With h = 5, we have: C = 1.5(5) + 2.25 C = 7.5 + 2.25 C = 9.75
the cost of a buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 k
the cost of a buffet at a restaurant is different for adults and kids. the bill for 2 adults and 3 kids is $51. the bill for 3 adults and 1 kid is $45. what is the cost per adult and per kid? Let the cost for each adult be a Let the cost for each kid be k We're given two equations: [LIST=1] [*]2a + 3k = 51 [*]3a + k = 45 [/LIST] To solve this simultaneous set of equations, we can use three methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2a+%2B+3k+%3D+51&term2=3a+%2B+k+%3D+45&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we use, we get the same answer: [LIST] [*]a = [B]12[/B] [*]k = [B]9[/B] [/LIST]
The cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a ga
The cost of a gallon of milk (m) is .50 more than 5 times the cost of a gallon of water (w). If a gallon of milk cost 3.75, what is the cost of a gallon of water? We're given: m = 5w + 0.50 m = $3.75 Set them equal to each other: 5w + 0.50 = 3.75 [URL='https://www.mathcelebrity.com/1unk.php?num=5w%2B0.50%3D3.75&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 0.65[/B]
The cost of tuition at Johnson Community College is $160 per credit hour. Each student also has to p
The cost of tuition at Johnson Community College is $160 per credit hour. Each student also has to pay $50 in fees. Model the cost, C, for x credit hours taken. Set up cost equation, where h is the number of credit hours: [B]C = 50 + 160h[/B]
The cost to rent a construction crane is 450 per day plus 150 per hour. What is the maximum number o
The cost to rent a construction crane is 450 per day plus 150 per hour. What is the maximum number of hours the crane can be used each day if the rental cost is not to exceed 1650 per day? Set up the cost function where h is the number of hours: C(h) = 150h + 450 We want C(h) <= 1650: 150h + 450 <= 1650 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=150h%2B450%3C%3D1650&pl=Solve']equation/inequality solver[/URL], we get: [B]h <= 8[/B]
The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each
The dance committee of pine bluff middle school earns $72 from a bake sale and will earn $4 for each ticket sold they sell to the Spring Fling dance. The dance will cost $400 Let t be the number of tickets sold. We have a Revenue function R(t): R(t) = 4t + 72 We want to know t such that R(t) = 400. So we set R(t) = 400: 4t + 72 = 400 [URL='https://www.mathcelebrity.com/1unk.php?num=4t%2B72%3D400&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]t = 82[/B]
The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is
The denominator of a fraction is 4 more than the numerator. If 4 is added to the numerator and 7 is added to the denominator, the value of the fraction is 1/2. Find the original fraction. Let the original fraction be n/d. We're given: [LIST=1] [*]d = n + 4 [*](n + 4) / (d + 7) = 1/2 [/LIST] Cross multiply Equation 2: 2(n + 4) = d + 7 2n + 8 = d + 7 Now substitute equation (1) into tihs: 2n + 8 = (n + 4) + 7 2n + 8 = n + 11 [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B8%3Dn%2B11&pl=Solve']Type this equation into our search engine[/URL], and we get: n = 3 This means from equation (1), that: d = 3 + 4 d = 7 So our original fraction n/d = [B]3/7[/B]
The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. Wh?
The difference between 2 numbers is 108. 6 times the smaller is equal to 2 more than the larger. What are the numbers? Let the smaller number be x. Let the larger number be y. We're given: [LIST=1] [*]y - x = 108 [*]6x = y + 2 [/LIST] Rearrange (1) by adding x to each side: [LIST=1] [*]y = x + 108 [/LIST] Substitute this into (2): 6x = x + 108 + 2 Combine like terms 6x = x +110 Subtract x from each side: 5x = 110 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%3D110&pl=Solve']Plugging this equation into our search engine[/URL], we get: x = [B]22[/B]
The difference between a and b is 10
The difference between a and b is 10. The problem asks for an algebraic expression. Let's take each piece one by one: [I]Difference between[/I] means we subtract: a - b The phrase [I]is [/I]means an equation, so we set a - b equal to 10 [B]a - b = 10[/B]
The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is
The difference between two numbers is 25. The smaller number is 1/6th of the larger number. What is the value of the smaller number Let the smaller number be s. Let the larger number be l. We're given two equations: [LIST=1] [*]l - s = 25 [*]s = l/6 [/LIST] Plug in equation (2) into equation (1): l - l/6 = 25 Multiply each side of the equation by 6 to remove the fraction: 6l - l = 150 To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=6l-l%3D150&pl=Solve']type this equation into our search engine[/URL] and we get: l = 30 To solve for s, we plug in l = 30 into equation (2) above: s = 30/6 [B]s = 5[/B]
The difference between two positive numbers is 5 and the square of their sum is 169
The difference between two positive numbers is 5 and the square of their sum is 169. Let the two positive numbers be a and b. We have the following equations: [LIST=1] [*]a - b = 5 [*](a + b)^2 = 169 [*]Rearrange (1) by adding b to each side. We have a = b + 5 [/LIST] Now substitute (3) into (2): (b + 5 + b)^2 = 169 (2b + 5)^2 = 169 [URL='https://www.mathcelebrity.com/community/forums/calculator-requests.7/create-thread']Run (2b + 5)^2 through our search engine[/URL], and you get: 4b^2 + 20b + 25 Set this equal to 169 above: 4b^2 + 20b + 25 = 169 [URL='https://www.mathcelebrity.com/quadratic.php?num=4b%5E2%2B20b%2B25%3D169&pl=Solve+Quadratic+Equation&hintnum=+0']Run that quadratic equation in our search engine[/URL], and you get: b = (-9, 4) But the problem asks for [I]positive[/I] numbers. So [B]b = 4[/B] is one of our solutions. Substitute b = 4 into equation (1) above, and we get: a - [I]b[/I] = 5 [URL='https://www.mathcelebrity.com/1unk.php?num=a-4%3D5&pl=Solve']a - 4 = 5[/URL] [B]a = 9 [/B] Therefore, we have [B](a, b) = (9, 4)[/B]
The difference in Julies height and 9 is 48 letting j be Julie's height
The difference in Julies height and 9 is 48 letting j be Julie's height Step 1: If Julie's height is represented with the variable j, then we subtract 9 from j since the phrase [I]difference[/I] means we subtract: j - 9 Step 2: The word [I]is[/I] means an equation, so we set j - 9 equal to 48 for our final algebraic expression: [B]j - 9 = 48[/B]
The difference of 100 and x is 57
The difference of 100 and x means we subtract x from 100: 100 - x Is means equal to, so we set our expression above equal to 57 [B]100 - x = 57 [/B] If you want to solve for x, use our [URL='http://www.mathcelebrity.com/1unk.php?num=100-x%3D57&pl=Solve']equation calculator[/URL]
The difference of 2 positive numbers is 54. The quotient obtained on dividing the 1 by the other is
The difference of 2 positive numbers is 54. The quotient obtained on dividing the 1 by the other is 4. Find the numbers. Let the numbers be x and y. We have: [LIST] [*]x - y = 54 [*]x/y = 4 [*]Cross multiply x/y = 4 to get x = 4y [*]Now substitute x = 4y into the first equation [*](4y) - y = 54 [*]3y = 54 [*]Divide each side by 3 [*][B]y = 18[/B] [*]If x = 4y, then x = 4(18) [*][B]x = 72[/B] [/LIST]
The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown n
The difference of a number times 3 and 6 is equal to 7 . Use the variable w for the unknown number. The phrase a number uses the variable w. 3 times w is written as 3w The difference of 3w and 6 is written as 3w - 6 Set this equal to 7 [B]3w - 6 = 7 [/B] This is our algebraic expression. To solve this equation for w, we [URL='http://www.mathcelebrity.com/1unk.php?num=3w-6%3D7&pl=Solve']type the algebraic expression into our search engine[/URL].
The difference of two numbers is 12 and their mean is 15. Find the two numbers
The difference of two numbers is 12 and their mean is 15. Find the two numbers. Let the two numbers be x and y. We're given: [LIST=1] [*]x - y = 12 [*](x + y)/2 = 15. <-- Mean is an average [/LIST] Rearrange equation 1 by adding y to each side: x - y + y = y + 12 Cancelling the y's on the left side, we get: x = y + 12 Now substitute this into equation 2: (y + 12 + y)/2 = 15 Cross multiply: y + 12 + y = 30 Group like terms for y: 2y + 12 = 30 [URL='https://www.mathcelebrity.com/1unk.php?num=2y%2B12%3D30&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]y = 9[/B] Now substitute this into modified equation 1: x = y + 12 x = 9 + 12 [B]x = 21[/B]
The difference of two numbers is 720. The smaller of the numbers is 119. What is the other number?
The difference of two numbers is 720. The smaller of the numbers is 119. What is the other number? Let the larger number be l. We're given: l - 119 = 720 [URL='https://www.mathcelebrity.com/1unk.php?num=l-119%3D720&pl=Solve']We type this equation into the search engine[/URL] and we get: l = [B]839[/B]
the difference of x and 5 is 2 times of x
the difference of x and 5 is 2 times of x The difference of x and 5 means we subtract 5 from x x - 5 The word [I]is[/I] means an equation, so we set x - 5 equal to 2 times x [B]x - 5 = 2x[/B]
The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased by x cm and its width i
The dimensions of a rectangle are 30 cm and 18 cm. When its length decreased by x cm and its width is increased by x cm, its area is increased by 35 sq. cm. a. Express the new length and the new width in terms of x. b. Express the new area of the rectangle in terms of x. c. Find the value of x. Calculate the current area. Using our [URL='https://www.mathcelebrity.com/rectangle.php?l=30&w=18&a=&p=&pl=Calculate+Rectangle']rectangle calculator with length = 30 and width = 18[/URL], we get: A = 540 a) Decrease length by x and increase width by x, and we get: [LIST] [*]length = [B]30 - x[/B] [*]width = [B]18 + x[/B] [/LIST] b) Our new area using the lw = A formula is: (30 - x)(18 + x) = 540 + 35 Multiplying through and simplifying, we get: 540 - 18x + 30x - x^2 = 575 [B]-x^2 + 12x + 540 = 575[/B] c) We have a quadratic equation. To solve this, [URL='https://www.mathcelebrity.com/quadratic.php?num=-x%5E2%2B12x%2B540%3D575&pl=Solve+Quadratic+Equation&hintnum=+0']we type it in our search engine, choose solve[/URL], and we get: [B]x = 5 or x = 7[/B] Trying x = 5, we get: A = (30 - 5)(18 + 5) A = 25 * 23 A = 575 Now let's try x = 7: A = (30 - 7)(18 + 7) A = 23 * 25 A = 575 They both check out. So we can have
The domain of a relation is all even negative integers greater than -9. The range y of the relation
The domain of a relation is all even negative integers greater than -9. The range y of the relation is the set formed by adding 4 to the numbers in the domain. Write the relation as a table of values and as an equation. The domain is even negative integers greater than -9: {-8, -6, -4, -2} Add 4 to each x for the range: {-8 + 4 = -4, -6 + 4 = -2. -4 + 4 = 0, -2 + 4 = 2} For ordered pairs, we have: (-8, -4) (-6, -2) (-4, 0) (-2, 2) The equation can be written: y = x + 4 on the domain (x | x is an even number where -8 <= x <= -2)
The enrollment at High School R has been increasing by 20 students per year. High School R currently
The enrollment at High School R has been increasing by 20 students per year. High School R currently has 200 students. High School T has 400 students and is decreasing 30 students per year. When will the two school have the same enrollment of students? Set up the Enrollment function E(y) where y is the number of years. [U]High School R:[/U] [I]Increasing[/I] means we add E(y) = 200 + 20y [U]High School T:[/U] [I]Decreasing[/I] means we subtract E(y) = 400 - 30y When the two schools have the same enrollment, we set the E(y) functions equal to each other 200 + 20y = 400 - 30y To solve this equation for y, we [URL='https://www.mathcelebrity.com/1unk.php?num=200%2B20y%3D400-30y&pl=Solve']type it in our search engine[/URL] and we get: y = [B]4[/B]
the equation of a line is y = mx + 4. find m if the line passes through (-5,0)
the equation of a line is y = mx + 4. find m if the line passes through (-5,0) Plug in our numbers of x = -5, and y = 0: -5m + 4 = 0 To solve for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=-5m%2B4%3D0&pl=Solve']plug in this equation into our search engine[/URL] and we get: [B]m = 0.8 or 4/5[/B] so our line equation becomes: [B]y = 4/5x + 4[/B]
The first group orders 3 pizzas and 4 drinks for $33.50. The second group orders 5 pizzas and 6 drin
The first group orders 3 pizzas and 4 drinks for $33.50. The second group orders 5 pizzas and 6 drinks for $54. Find the cost for each pizza and each drink Assumptions: [LIST] [*]Let the cost of each pizza be p [*]Let the cost of each drink be d [/LIST] Givens: [LIST=1] [*]4d + 3p = 33.50 [*]6d + 5p = 54 [/LIST] We have a simultaneous group of equations. To solve this, we can use 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=4d+%2B+3p+%3D+33.50&term2=6d+%2B+5p+%3D+54&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we use, we get the same answer: [LIST] [*]d = [B]$2.75[/B] [*]p = [B]$7.5[/B] [/LIST]
The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The seco
The first plan has $14 monthly fee and charges an additional $.14 for each minute of calls. The second plan had a $21 monthly fee and charges an additional $.10 for each minute of calls. For how many minutes of calls will the cost of the two plans be equal? Set up the cost equation C(m) for the first plan, where m is the amount of minutes you use C(m) = 0.14m + 14 Set up the cost equation C(m) for the second plan, where m is the amount of minutes you use C(m) = 0.10m + 21 Set them equal to each other: 0.14m + 14 = 0.10m + 21 [URL='https://www.mathcelebrity.com/1unk.php?num=0.14m%2B14%3D0.10m%2B21&pl=Solve']Typing this equation into our search engine[/URL], we get: m = [B]175[/B]
The fixed costs to produce a certain product are 15,000 and the variable costs are $12.00 per item.
The fixed costs to produce a certain product are 15,000 and the variable costs are $12.00 per item. The revenue for a certain product is $27.00 each. If the company sells x products, then what is the revenue equation? R(x) = Revenue per item x number of products sold [B]R(x) = 27x[/B]
The flu is starting to hit Lanberry. Currently, there are 894 people infected, and that number is gr
The flu is starting to hit Lanberry. Currently, there are 894 people infected, and that number is growing at a rate of 5% per day. Overall, how many people will have gotten the flu in 5 days? Our exponential equation for the Flu at day (d) is: F(d) = Initial Flu cases * (1 + growth rate)^d Plugging in d = 5, growth rate of 5% or 0.05, and initial flu cases of 894 we have: F(5) = 894 * (1 + 0.05)^5 F(5) = 894 * (1.05)^5 F(5) = 894 * 1.2762815625 F(5) = [B]1141[/B]
The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the f
The fraction has a value of 3/5. The sum of the numerator and the denominator was 40. What was the fraction? We're given two equations with a fraction with numerator (n) and denominator (d): [LIST=1] [*]n + d = 40 [*]n/d = 3/5 [/LIST] Cross multiply equation 2, we get: 5n = 3d Divide each side by 5: 5n/5 = 3d/5 n = 3d/5 Substitute this into equation 1: 3d/5 + d = 40 Multiply through both sides of the equation by 5: 5(3d/5) = 5d = 40 * 5 3d + 5d =200 To solve this equation for d, we [URL='https://www.mathcelebrity.com/1unk.php?num=3d%2B5d%3D200&pl=Solve']type it in our search engine and we get[/URL]: d = [B]25 [/B] Now substitute that back into equation 1: n + 25 = 40 Using [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B25%3D40&pl=Solve']our equation solver again[/URL], we get: n = [B]15[/B]
the fuel tank of a jet used gas at a constant rate of 300 gallons for each hour of flight. the tank
the fuel tank of a jet used gas at a constant rate of 300 gallons for each hour of flight. the tank can hold a maximum of 2400 gallons of gas. write an equation representing the amount of fuel left in the tank as a function of the number of hours spent flying. We have an equation F(h) where h is the number of hours since the flight took off: [B]F(h) = 2400 - 300h[/B]
The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the ba
The function P(x) = -30x^2 + 360x + 785 models the profit, P(x), earned by a theatre owner on the basis of a ticket price, x. Both the profit and the ticket price are in dollars. What is the maximum profit, and how much should the tickets cost? Take the [URL='http://www.mathcelebrity.com/dfii.php?term1=-30x%5E2+%2B+360x+%2B+785&fpt=0&ptarget1=0&ptarget2=0&itarget=0%2C1&starget=0%2C1&nsimp=8&pl=1st+Derivative']derivative of the profit function[/URL]: P'(x) = -60x + 360 We find the maximum when we set the profit derivative equal to 0 -60x + 360 = 0 Subtract 360 from both sides: -60x = -360 Divide each side by -60 [B]x = 6 <-- This is the ticket price to maximize profit[/B] Substitute x = 6 into the profit equation: P(6) = -30(6)^2 + 360(6) + 785 P(6) = -1080 + 2160 + 785 [B]P(6) = 1865[/B]
The graph of a polynomial f(x) = (2x - 3)(x - 4)(x + 3) has x-intercepts at 3 values. What are they?
The graph of a polynomial f(x) = (2x - 3)(x - 4)(x + 3) has x-intercepts at 3 values. What are they? A few things to note: [LIST] [*]X-intercepts are found when y (or f(x)) is 0. [*]On the right side, we have 3 monomials. [*]Therefore, y or f(x) could be 0 when [U]any[/U] of these monomials is 0 [/LIST] The 3 monomials are: [LIST=1] [*]2x - 3 = 0 [*]x - 4 = 0 [*]x + 3 = 0 [/LIST] Find all 3 x-intercepts: [LIST=1] [*]2x - 3 = 0. [URL='https://www.mathcelebrity.com/1unk.php?num=2x-3%3D0&pl=Solve']Using our equation calculator[/URL], we see that x = [B]3/2 or 1.5[/B] [*]x - 4 = 0 [URL='https://www.mathcelebrity.com/1unk.php?num=x-4%3D0&pl=Solve']Using our equation calculator[/URL], we see that x = [B]4[/B] [*]x + 3 = 0 [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B3%3D0&pl=Solve']Using our equation calculator[/URL], we see that x = [B]-3[/B] [/LIST] So our 3 x-intercepts are: x = [B]{-3, 3/2, 4}[/B]
The Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39
The Lakers recently scored 81 points. Their points came from 2 and 3 point baskets. If they made 39 baskets total, how many of each basket did they make? Let x = 2 point baskets and y = 3 point baskets. We have the following given equations: [LIST=1] [*]x + y = 39 [*]2x + 3y = 81 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=x%2By%3D39&term2=2x+%2B+3y+%3D+81&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [B]x = 36 <-- 2 point baskets y = 3 <-- 3[B] point baskets [/B][/B] To confirm our work: [LIST=1] [*]36 + 3 = 39 [*]2(36) + 3(3) = 72 + 9 = 81 [/LIST]
The Lakewood library has $8,040 to buy science magazines. If each magazine costs $3, how many magazi
The Lakewood library has $8,040 to buy science magazines. If each magazine costs $3, how many magazines will the library be able to buy? Let number of magazines be m. We know that: Cost per magazine * m = Total Cost We're given Total Cost = 8040 and Cost per magazine = 3, so we have 3m = 8040 To solve this equation for m, we [URL='https://www.mathcelebrity.com/1unk.php?num=3m%3D8040&pl=Solve']type it in our math engine[/URL] and we get: m = [B]2680[/B]
The larger of 2 numbers is 1 more than 3 times the smaller number
The larger of 2 numbers is 1 more than 3 times the smaller number. Let the larger number be l. Let the smaller number be s. The algebraic expression is: 3 times the smaller number is written as: 3s 1 more than that means we add 1 3s + 1 Our final algebraic expression uses the word [I]is[/I] meaning an equation. So we set l equal to 3s + 1 [B]l = 3s + 1[/B]
The left and right page numbers of an open book are two consecutive integers whose sum is 403. Find
The left and right page numbers of an open book are two consecutive integers whose sum is 403. Find these page numbers. Page numbers left and right are consecutive integers. So we want to find a number n and n + 1 where: n + n + 1 = 403 Combining like terms, we get: 2n + 1 = 403 Typing that equation into our search engine, we get: [B]n = 201[/B] This is our left hand page. Our right hand page is: 201 + 1 = [B]202[/B]
The length of a rectangle is equal to triple the width. Find the length of the rectangle if the peri
The length of a rectangle is equal to triple the width. Find the length of the rectangle if the perimeter is 80 inches. The perimeter (P) of a rectangle is: 2l + 2w = P We're given two equations: [LIST=1] [*]l = 3w [*]2l + 2w = 80 [/LIST] We substitute equation 1 into equation 2 for l: 2(3w) + 2w = 80 6w + 2w = 80 To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B2w%3D80&pl=Solve']type it in our search engine[/URL] and we get: w = 10 To solve for the length (l), we substitute w = 10 into equation 1 above: l = 3(10) l = [B]30[/B]
The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 fee
The length of a rectangular building is 6 feet less than 3 times the width. The perimeter is 120 feet. Find the width and length of the building. P = 2l + 2w Since P = 120, we have: (1) 2l + 2w = 120 We are also given: (2) l = 3w - 6 Substitute equation (2) into equation (1) 2(3w - 6) + 2w = 120 Multiply through: 6w - 12 + 2w = 120 Combine like terms: 8w - 12 = 120 Add 12 to each side: 8w = 132 Divide each side by 8 to isolate w: w =16.5 Now substitute w into equation (2) l = 3(16.5) - 6 l = 49.5 - 6 l = 43.5 So (l, w) = (43.5, 16.5)
The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft�
The length of a wooden frame is 1 foot longer than its width and its area is equal to 12ft� The frame is a rectangle. The area of a rectangle is A = lw. So were given: [LIST=1] [*]l = w + 1 [*]lw = 12 [/LIST] Substitute equation (1) into equation (2) for l: (w + 1) * w = 12 Multiply through and simplify: w^2 + w = 12 We have a quadratic equation. To solve for w, we type this equation into our search engine and we get two solutions: w = 3 w = -4 Since width cannot be negative, we choose the positive result and have: w = [B]3[/B] To solve for length, we plug w = 3 into equation (1) above and get: l = 3 + 1 l = [B]4[/B]
The length of Sally�s garden is 4 meters greater than 3 times the width. The perimeter of her garden
The length of Sally�s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters. Find the dimensions of Sally�s garden. Gardens have a rectangle shape. Perimeter of a rectangle is 2l + 2w. We're given: [LIST=1] [*]l = 3w + 4 [I](3 times the width Plus 4 since greater means add)[/I] [*]2l + 2w = 72 [/LIST] We substitute equation (1) into equation (2) for l: 2(3w + 4) + 2w = 72 Multiply through and simplify: 6w + 8 + 2w = 72 (6 +2)w + 8 = 72 8w + 8 = 72 To solve this equation for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=8w%2B8%3D72&pl=Solve']type it in our search engine[/URL] and we get: w = [B]8 [/B] To solve for l, we substitute w = 8 above into Equation (1): l = 3(8) + 4 l = 24 + 4 l = [B]28[/B]
The length of Sally�s garden is 4 meters greater than 3 times the width. The perimeter of her garden
The length of Sally�s garden is 4 meters greater than 3 times the width. The perimeter of her garden is 72 meters A garden is a rectangle, which has perimeter P of: P = 2l + 2w With P = 72, we have: 2l + 2w = 72 We're also given: l = 3w + 4 We substitute this into the perimeter equation for l: 2(3w + 4) + 2w = 72 6w + 8 + 2w = 72 To solve this equation for w, we t[URL='https://www.mathcelebrity.com/1unk.php?num=6w%2B8%2B2w%3D72&pl=Solve']ype it in our search engine[/URL] and we get: w =[B] 8[/B] Now, to solve for l, we substitute w = 8 into our length equation above: l = 3(8) + 4 l = 24 + 4 l = [B]28[/B]
The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length a
The length of the flag is 2 cm less than 7 times the width. The perimeter is 60cm. Find the length and width. A flag is a rectangle shape. So we have the following equations Since P = 2l + 2w, we have 2l + 2w = 60 l = 7w - 2 Substitute Equation 1 into Equation 2: 2(7w -2) + 2w = 60 14w - 4 + 2w = 60 16w - 4 = 60 Add 4 to each side 16w = 64 Divide each side by 16 to isolate w w = 4 Which means l = 7(4) - 2 = 28 - 2 = 26
the lowest temperature on may 15 is 2/3 as warm as the warmest temperature on may 15. the lowest tem
the lowest temperature on may 15 is 2/3 as warm as the warmest temperature on may 15. the lowest temperature on may 15 is 60F what is the warmest temperature on may 15? Set up an equation where w is the warmest temperature on May 15: 60 = 2/3w [URL='https://www.mathcelebrity.com/1unk.php?num=60%3D2%2F3w&pl=Solve']Type this equation into our search engine[/URL], and we get: w = [B]90[/B]
The mean age of 5 people in a room is 28 years. A person enters the room. The mean age is now 32. W
The mean age of 5 people in a room is 28 years. A person enters the room. The mean age is now 32. What is the age of the person who entered the room? The sum of the 5 people's scores is S. We know: S/5 = 28 Cross multiply: S = 140 We're told that: (140 + a)/6 = 32 Cross multiply: 140 + a = 192 [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D192&pl=Solve']Type this equation into our search engine[/URL], we get: a = [B]52[/B]
The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. Wh
The mean age of 5 people in a room is 32 years. A person enters the room. The mean age is now 40. What is the age of the person who entered the room? Mean = Sum of Ages in Years / Number of People 32 = Sum of Ages in Years / 5 Cross multiply: Sum of Ages in Years = 32 * 5 Sum of Ages in Years = 160 Calculate new mean after the next person enters the room. New Mean = (Sum of Ages in Years + New person's age) / (5 + 1) Given a new Mean of 40, we have: 40 = (160 + New person's age) / 6 Cross multiply: New Person's Age + 160 = 40 * 6 New Person's Age + 160 = 240 Let the new person's age be n. We have: n + 160 = 240 To solve for n, [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B160%3D240&pl=Solve']we type this equation into our search engine[/URL] and we get: n = [B]80[/B]
The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. Wh
The mean age of 5 people in a room is 38 years. A person enters the room. The mean age is now 39. What is the age of the person who entered the room? The mean formulas is denoted as: Mean = Sum of Ages / Total People We're given Mean = 38 and Total People = 5, so we plug in our numbers: 28 = Sum of Ages / 5 Cross multiply, and we get: Sum of Ages = 28 * 5 Sum of Ages = 140 One more person enters the room. The mean age is now 39. Set up our Mean formula: Mean = Sum of Ages / Total People With a new Mean of 39 and (5 + 1) = 6 people, we have: 39 = Sum of Ages / 6 But the new sum of Ages is the old sum of ages for 5 people plus the new age (a): Sum of Ages = 140 + a So we have: 29 = (140 + a)/6 Cross multiply: 140 + a = 29 * 6 140 + a = 174 To solve for a, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2Ba%3D174&pl=Solve']we type this equation into our search engine[/URL] and we get: a = [B]34[/B]
The mean of two numbers is 49.1. The first number is 18.3. What is the second number
The mean of two numbers is 49.1. The first number is 18.3. What is the second number We call the second number n. Since the mean is an average, in this case 2 numbers, we have: (18.3 + n)/2 = 49.1 Cross multiply: 18.3 + n = 98.2 [URL='https://www.mathcelebrity.com/1unk.php?num=18.3%2Bn%3D98.2&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]n = 79.9[/B]
The perimeter of a college basketball court is 102 meters and the length is twice as long as the wid
The perimeter of a college basketball court is 102 meters and the length is twice as long as the width. What are the length and width? A basketball court is a rectangle. The perimeter P is: P = 2l + 2w We're also given l = 2w and P = 102. Plug these into the perimeter formula: 2(2w) + 2w = 102 4w + 2w = 102 6w = 102 [URL='https://www.mathcelebrity.com/1unk.php?num=6w%3D102&pl=Solve']Typing this equation into our calculator[/URL], we get: [B]w = 17[/B] Plug this into the l = 2w formula, we get: l = 2(17) [B]l = 34[/B]
The perimeter of a garden is 70 meters. Find its actual dimensions if its length is 5 meters longer
The perimeter of a garden is 70 meters. Find its actual dimensions if its length is 5 meters longer than twice its width. Let w be the width, and l be the length. We have: P = l + w. Since P = 70, we have: [LIST=1] [*]l + w = 70 [*]l = 2w + 5 [/LIST] Plug (2) into (1) 2w + 5 + w = 70 Group like terms: 3w + 5 = 70 Using our [URL='https://www.mathcelebrity.com/1unk.php?num=3w%2B5%3D70&pl=Solve']equation calculator[/URL], we get [B]w = 21.66667[/B]. Which means length is: l = 2(21.6667) + 5 l = 43.33333 + 5 [B]l = 48.3333[/B]
The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it?
The perimeter of a poster is 20 feet. The poster is 6 feet tall. How wide is it? [U]Assumptions and givens:[/U] [LIST] [*]The poster has a rectangle shape [*]l = 6 [*]P = 20 [*]The perimeter of a rectangle (P) is: 2l + 2w = P [/LIST] Plugging in our l and P values, we get: 2(6) + 2w = 20 Multiplying through and simplifying, we get: 12 + 2w = 20 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=12%2B2w%3D20&pl=Solve']type this equation into our search engine [/URL]and we get: w = [B]4[/B]
The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Fin
The perimeter of a rectangle is 400 meters. The length is 15 meters less than 4 times the width. Find the length and the width of the rectangle. l = 4w - 15 Perimeter = 2l + 2w Substitute, we get: 400 = 2(4w - 15) + 2w 400 = 8w - 30 + 2w 10w - 30 = 400 Add 30 to each side 10w = 370 Divide each side by 10 to isolate w w = 37 Plug that back into our original equation to find l l = 4(37) - 15 l = 148 - 15 l = 133 So we have (l, w) = (37, 133)
The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is
The perimeter of a rectangle parking lot is 340 m. If the length of the parking lot is 97 m, what is it�s width? The formula for a rectangles perimeter P, is: P = 2l + 2w where l is the length and w is the width. Plugging in our P = 340 and l = 97, we have: 2(97) + 2w = 340 Multiply through, we get: 2w + 194 = 340 [URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B194%3D340&pl=Solve']Type this equation into our search engine[/URL], we get: [B]w = 73[/B]
The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it?
The perimeter of a rectangular bakery is 204 feet. It is 66 feet long. How wide is it? Set up the perimeter equation: 2l + 2w = P Given P = 204 and l = 66, we have: 2(66) + 2w = 204 2w + 132 = 204 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B132%3D204&pl=Solve']equation solver,[/URL] we get w = [B]36[/B].
The perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find the
The perimeter of a rectangular field is 220 yd. the length is 30 yd longer than the width. Find the dimensions We are given the following equations: [LIST=1] [*]220 = 2l + 2w [*]l = w + 30 [/LIST] Plug (1) into (2) 2(w + 30) + 2w = 220 2w + 60 + 2w = 220 Combine like terms: 4w + 60 = 220 [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B60%3D220&pl=Solve']Plug 4w + 60 = 220 into the search engine[/URL], and we get [B]w = 40[/B]. Now plug w = 40 into equation (2) l = 40 + 30 [B]l = 70[/B]
The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is
The perimeter of a rectangular field is 250 yards. If the length of the field is 69 yards, what is its width? Set up the rectangle perimeter equation: P = 2l + 2w For l = 69 and P = 250, we have: 250= 2(69) + 2w 250 = 138 + 2w Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2w%2B138%3D250&pl=Solve']equation solver[/URL], we get: [B]w = 56 [/B]
The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it�s length
The perimeter of a rectangular field is 300m. If the width of the field is 59m, what is it�s length? Set up the perimeter (P) of a rectangle equation given length (l) and width (w): 2l + 2w = P We're given P = 300 and w = 59. Plug these into the perimeter equation: 2l + 2(59) = 300 2l + 118 = 300 [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B118%3D300&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]l = 91[/B]
The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it?
The perimeter of a rectangular notecard is 16 inches. The notecard is 5 inches wide. How tall is it? Perimeter of a rectangle P is: P = 2l + 2w We have: 2l + 2w = 16 We are given w = 5, so we have: 2l + 2(5) = 16 2l + 10 = 16 [URL='https://www.mathcelebrity.com/1unk.php?num=2l%2B10%3D16&pl=Solve']Plugging this into our equation calculator[/URL], we get [B]l = 3[/B].
The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. Wh
The perimeter of a rectangular outdoor patio is 54 ft. The length is 3 ft greater than the width. What are the dimensions of the patio? Perimeter of a rectangle is: P = 2l + 2w We're given l = w + 3 and P = 54. So plug this into our perimeter formula: 54= 2(w + 3) + 2w 54 = 2w + 6 + 2w Combine like terms: 4w + 6 = 54 [URL='https://www.mathcelebrity.com/1unk.php?num=4w%2B6%3D54&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 12[/B] Plug this into our l = w + 3 formula: l = 12 + 3 [B]l = 15[/B]
The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, wh
The perimeter of a rectangular parking lot is 258 meters. If the length of the parking lot is 71, what is its width? The perimeter for a rectangle (P) is given as: 2l + 2w = P We're given P = 258 and l = 71. Plug these values in: 2(71) + 2w = 258 142 + 2w = 258 [URL='https://www.mathcelebrity.com/1unk.php?num=142%2B2w%3D258&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]w = 58[/B]
The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it?
The perimeter of a rectangular shelf is 60 inches. The shelf is 7 inches deep. How wide is it? The perimeter for a rectangle is given below: P = 2l + 2w We're given l = 7 and P = 60. Plug this into the perimeter formula: 60 = 2(7) + 2w 60 = 14 + 2w Rewritten, it's 2w + 14 = 60. [URL='https://www.mathcelebrity.com/1unk.php?num=2w%2B14%3D60&pl=Solve']Typing this equation into our search engine[/URL], we get [B]w = 23[/B].
The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimete
The perpendicular height of a right-angled triangle is 70 mm longer than the base. Find the perimeter of the triangle if its area is 3000. [LIST] [*]h = b + 70 [*]A = 1/2bh = 3000 [/LIST] Substitute the height equation into the area equation 1/2b(b + 70) = 3000 Multiply each side by 2 b^2 + 70b = 6000 Subtract 6000 from each side: b^2 + 70b - 6000 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=b%5E2%2B70b-6000%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: b = 50 and b = -120 Since the base cannot be negative, we use b = 50. If b = 50, then h = 50 + 70 = 120 The perimeter is b + h + hypotenuse Using the [URL='http://www.mathcelebrity.com/righttriangle.php?angle_a=&a=70&angle_b=&b=50&c=&pl=Calculate+Right+Triangle']right-triangle calculator[/URL], we get hypotenuse = 86.02 Adding up all 3 for the perimeter: 50 + 70 + 86.02 = [B]206.02[/B]
The point (1,5) is a solution to the equation 2y - x = 9
The point (1,5) is a solution to the equation 2y - x = 9 [B]Yes[/B], because: 2(5) - 1 ? 9 10 - 1 ? 9 9 = 9
the product of 2 less than a number and 7 is 13
the product of 2 less than a number and 7 is 13 Take this algebraic expression in [U]4 parts[/U]: Part 1 - The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x Part 2 - 2 less than a number means we subtract 2 from x x - 2 Part 3 - The phrase [I]product[/I] means we multiply x - 2 by 7 7(x - 2) Part 4 - The phrase [I]is[/I] means an equation, so we set 7(x - 2) equal to 13 [B]7(x - 2) = 13[/B]
the quotient of 3 and u is equal to 52 divided by u
the quotient of 3 and u is equal to 52 divided by u Take this algebraic expression in 3 parts: [LIST=1] [*]The quotient of 3 and u means we divide 3 by u: 3/u [*]52 divided by u means we divide 52 by u: 52/u [*]The phrase [I]is equal to[/I] means an equation, so we set (1) equal to (2) [/LIST] [B]3/u = 52/u[/B]
the quotient of 4 more than a number and 7 is 10
the quotient of 4 more than a number and 7 is 10 Take this algebraic expression in pieces: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 4 more than a number means we add 4 to x: x + 4 The quotient of 4 more than a number and 7 means we divide x + 4 by 7 (x + 4)/7 The word [I]is[/I] means an equation, so we set (x + 4)/7 equal to 10 [B](x + 4)/7 = 10[/B]
the quotient of x and y is equal to the sum of a and b
the quotient of x and y is equal to the sum of a and b The quotient of x and y: x/y The sum of a and b: a + b The phrase [I]is equal to[/I] means an equation, so we set x/y equal to a + b: [B]x/y = a + b[/B]
The Radio City Music Hall is selling tickets to Kayla�s premiere at the Rockettes. On the first day
The Radio City Music Hall is selling tickets to Kayla�s premiere at the Rockettes. On the first day of ticket sales they sold 3 senior citizen tickets and 9 child tickets for a total of $75. It took in $67 on the second day by selling 8 senior citizen tickets and 5 child tickets. What is the price of each senior citizen ticket and each child ticket? Let the cost of child tickets be c Let the cost of senior tickets be s Since revenue = cost * quantity, we're given two equations: [LIST=1] [*]9c + 3s = 75 [*]5c + 8s = 67 [/LIST] To solve this simultaneous group of equations, we can use 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=9c+%2B+3s+%3D+75&term2=5c+%2B+8s+%3D+67&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we use, we get the same answer: [LIST] [*][B]c = 7[/B] [*][B]s = 4[/B] [/LIST]
The sales price of a new compact disc player is $210 at a local discount store. At the store where t
The sales price of a new compact disc player is $210 at a local discount store. At the store where the sale is going on, each new cd is on sale for $11. If Kyle purchases a player and some cds for $243 how many cds did he purchase? If Kyle bought the player, he has 243 - 210 = 33 left over. Each cd is 11, so set up an equation to see how many CDs he bought: 11x = 33 Divide each side by 11 [B]x = 3[/B]
The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00.
The school is selling potted plants as a fundraiser. Kara sold 12 ferns and 8 ivy plants for 260.00. Paul sold 15 ivy plants and 6 ferns for 240. What�s the selling price of each plant. Let the cost of each fern be f Let the cost of each ivy plant be I We're given: [LIST=1] [*]12f + 8i = 260 [*]15i + 6f = 240 [/LIST] To solve this system of equations, we can use 3 methods: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=12f+%2B+8i+%3D+260&term2=15f+%2B+6i+%3D+240&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get the same answer: [LIST] [*][B]f = 7.5[/B] [*][B]i= 21.25[/B] [/LIST]
The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for
The school yearbook costs $15 per book to produce with an overhead of $5500. The yearbook sells for $40. Write a cost and revenue function and determine the break-even point. [U]Calculate cost function C(b) with b as the number of books:[/U] C(b) = Cost per book * b + Overhead [B]C(b) = 15b + 5500[/B] [U]Calculate Revenue Function R(b) with b as the number of books:[/U] R(b) = Sales Price per book * b [B]R(b) = 40b[/B] [U]Calculate break even function E(b):[/U] Break-even Point = Revenue - Cost Break-even Point = R(b) - C(b) Break-even Point = 40b - 15b - 5500 Break-even Point = 25b - 5500 [U]Calculate break even point:[/U] Break-even point is where E(b) = 0. So we set 25b - 5500 equal to 0 25b - 5500 = 0 To solve for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=25b-5500%3D0&pl=Solve']type this equation into our search engine[/URL] and we get: [B]b = 220[/B]
The senior class at high school A and high school B planned separate trips to the state fair. There
The senior class at high school A and high school B planned separate trips to the state fair. There senior class and high school A rented and filled 10 vans and 6 buses with 276 students. High school B rented and filled 5 vans and 2 buses with 117 students. Every van had the same number of students in them as did the buses. How many students can a van carry?? How many students can a bus carry?? Let b be the number of students a bus can carry. Let v be the number of students a van can carry. We're given: [LIST=1] [*]High School A: 10v + 6b = 276 [*]High School B: 5v + 2b = 117 [/LIST] We have a system of equations. We can solve this 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=10v+%2B+6b+%3D+276&term2=5v+%2B+2b+%3D+117&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter which method we choose, we get: [LIST] [*][B]b = 21[/B] [*][B]v = 15[/B] [/LIST]
The square of a number increased by 7 is 23
The square of a number increased by 7 is 23 The phrase [I]a number [/I]means an arbitrary variable, let's call it x. x The square of a number means we raise x to the power of 2: x^2 [I]Increased by[/I] means we add 7 to x^2 x^2 + 7 The word [I]is[/I] means an equation. So we set x^2 + 7 equal to 23: [B]x^2 + 7 = 23[/B]
The Square of a positive integer is equal to the sum of the integer and 12. Find the integer
The Square of a positive integer is equal to the sum of the integer and 12. Find the integer Let the integer be x. [LIST] [*]The sum of the integer and 12 is written as x + 12. [*]The square of a positive integer is written as x^2. [/LIST] We set these equal to each other: x^2 = x + 12 Subtract x + 12 from each side: x^2 - x - 12 = 0 We have a quadratic function. [URL='https://www.mathcelebrity.com/quadratic.php?num=x%5E2-x-12%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Run it through our search engine[/URL] and we get x = 3 and x = -4. The problem asks for a positive integer, so we have [B]x = 3[/B]
The square of a positive integer minus twice its consecutive integer is equal to 22. find the intege
The square of a positive integer minus twice its consecutive integer is equal to 22. Find the integers. Let x = the original positive integer. We have: [LIST] [*]Consecutive integer is x + 1 [*]x^2 - 2(x + 1) = 22 [/LIST] Multiply through: x^2 - 2x - 2 = 22 Subtract 22 from each side: x^2 - 2x - 24 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2-2x-24%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we get: x = 6 and x = -4 Since the problem states [U]positive integers[/U], we use: x = 6 and x + 1 = 7 [B](6, 7)[/B]
the square root of twice a number is 4 less than the number
Write this out, let the number be x. sqrt(2x) = x - 4 since 4 less means subtract Square each side: sqrt(2x)^2 = (x - 4)^2 2x = x^2 - 8x + 16 Subtract 2x from both sides x^2 - 10x + 16 = 0 Using the [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2+-+10x+%2B+16+%3D+0&pl=Solve+Quadratic+Equation&hintnum=0']quadratic calculator[/URL], we get two potential solutions x = (2, 8) Well, 2 does not work, since sqrt(2*2) = 2 which is not 4 less than 2 However, 8 does work: sqrt(2*8) = sqrt(16) = 4, which is 4 less than the number 8.
The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers?
The sum of 2 consecutive numbers is 3 less than 3 times the first number. What are the numbers? Let the first number be x. And the second number be y. We're given: [LIST=1] [*]y = x + 1 [*]x + y = 3x - 3 (less 3 means subtract 3) [/LIST] Substitute (1) into (2): x + x + 1 = 3x - 3 Combine like terms: 2x + 1 = 3x - 3 [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B1%3D3x-3&pl=Solve']Type this equation into the search engine[/URL], we get: x = 4 Substituting x = 4 into equation 1: y = 4 + 1 y = 5 So (x, y) = [B](4, 5)[/B]
The sum of 2 numbers is 18. 3 times the greater number exceeds 4 times the smaller number by 5. Find
The sum of 2 numbers is 18. 3 times the greater number exceeds 4 times the smaller number by 5. Find the numbers. Let the first number be x. The second number is y. We have: [LIST=1] [*]x + y = 18 [*]3x = 4y + 5 [/LIST] Rearrange (2), by subtracting 4y from each side: 3x - 4y = 5 So we have a system of equations: [LIST=1] [*]x + y = 18 [*]3x - 4y = 5 [/LIST] Using our [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y+%3D+18&term2=3x+-+4y+%3D+5&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [B]x = 11 y = 7[/B]
the sum of 2 numbers is 5. 5 times the larger number plus 4 times the smaller number is 37. Find the
the sum of 2 numbers is 5. 5 times the larger number plus 4 times the smaller number is 37. Find the numbers Let the first small number be x. Let the second larger number be y. We're given: [LIST=1] [*]x + y = 5 [*]5y + 4x = 37 [/LIST] We can solve this 3 ways, using the following methods: [LIST=1] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=x+%2B+y%3D5&term2=5y+%2B+4x+%3D+37&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [B]x = -12 y = 17 [/B] Let's check our work using equation 1: -12 + 17 ? 5 5 = 5 <-- Check Let's check our work using equation 2: 5(17) + 4(-12) ? 37 85 - 48 ? 37 37 = 37 <-- Check
The sum of 2 numbers is 60. The larger number is thrice the smaller
The sum of 2 numbers is 60. The larger number is thrice the smaller. Let the 2 numbers be x and y, where x is the smaller number and y is the larger number. We are given: [LIST=1] [*]x + y = 60 [*]y = 3x [/LIST] Substitute (2) into (1): x + (3x) = 60 Combine like terms: 4x = 60 [URL='https://www.mathcelebrity.com/1unk.php?num=4x%3D60&pl=Solve']Type 4x = 60 into our search engine[/URL], and you get [B]x = 15[/B]. Substituting x = 15 into Equation (2) above, we get: y = 3(15) [B]y = 45 [/B] Check our work in Equation (1): 15 + 45 ? 60 60 = 60 Check our work in Equation (2): 45 ? 15(3) 45 = 45 The numbers check out, so our answer is [B](x, y) = (15, 45)[/B]
The sum of 2 numbers is 70. The difference of these numbers is 24. Write and solve a system of equat
The sum of 2 numbers is 70. The difference of these numbers is 24. Write and solve a system of equations to determine the numbers. Let the two numbers be x and y. We have the following equations: [LIST=1] [*]x + y = 70 [*]x - y = 24 [/LIST] Add (1) to (2): 2x = 94 Divide each side by 2 [B]x = 47[/B] Plug this into (1) 47 + y = 70 Subtract 47 from each side, we have: [B]y = 23[/B]
the sum of 23 and victor age is 59
the sum of 23 and victor age is 59 Let's Victor's age be a. The sum of 23 and Victor's age (a) mean we add a to 23: 23 + a The word [I]is[/I] means an equation, so we set 23 + a equal to 59: [B]23 + a = 59[/B] <-- This is our algebraic expression Now if the problem asks you to take it a step further and solve this for a, [URL='https://www.mathcelebrity.com/1unk.php?num=23%2Ba%3D59&pl=Solve']we type this equation into our search engine[/URL] and we get: [B]a = 36[/B]
the sum of 3 and 2x is 10
the sum of 3 and 2x is 10 The sum of 3 and 2x means we add 2x to 3: 3 + 2x The word [I]is[/I] means an equation, so we set 3 + 2x equal to 10 [B]3 + 2x = 10[/B]
The sum of 3, 7, and a number amounts to 16
The sum of 3, 7, and a number amounts to 16 Let the number be n. A sum means we add. We're given: 3 + 7 + n = 16 Grouping like terms, we get: n + 10 = 16 [URL='https://www.mathcelebrity.com/1unk.php?num=n%2B10%3D16&pl=Solve']Typing this equation into our search engine[/URL], we get: n = [B]6 [/B]
The sum of 5 odd consecutive numbers is 145
The sum of 5 odd consecutive numbers is 145. Let the first odd number be n. We have the other 4 odd numbers denoted as: [LIST] [*]n + 2 [*]n + 4 [*]n + 6 [*]n + 8 [/LIST] Add them all together n + (n + 2) + (n + 4) + (n + 6) + (n + 8) The sum of the 5 odd consecutive numbers equals 145 n + (n + 2) + (n + 4) + (n + 6) + (n + 8) = 145 Combine like terms: 5n + 20 = 145 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=5n%2B20%3D145&pl=Solve']equation solver[/URL], we get [B]n = 25[/B]. Using our other 4 consecutive odd numbers above, we get: [LIST] [*]27 [*]29 [*]31 [*]33 [/LIST] Adding the sum up, we get: 25 + 27 + 29 + 31 + 33 = 145. So our 5 odd consecutive number added to get 145 are [B]{25, 27, 29, 31, 33}[/B].
the sum of 6 and 7, plus 5 times a number, is -12
the sum of 6 and 7, plus 5 times a number, is -12 The sum of 6 and 7 means we add the two numbers: 6 + 7 This evaluates to 13 Next, we take 5 times a number. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. So we multiply x by 5: 5x The first two words say [I]the sum[/I], so we add 13 and 5x 13 + 5x The word [I]is[/I] means an equation, so we set 13 + 5x equal to -12 [B]13 + 5x = -12[/B] <-- This is our algebraic expression If the problem asks you to take it a step further and solve for x, then you [URL='https://www.mathcelebrity.com/1unk.php?num=13%2B5x%3D-12&pl=Solve']type this algebraic expression into our search engine[/URL] and you get: [B]x = -5[/B]
the sum of 7 times y and 3 is equal to 2
the sum of 7 times y and 3 is equal to 2 7 times y: 7y The sum of 7 times y and 3 means we add 3 to 7y 7y + 3 The phrase [I]is equal to[/I] means an equation, so we set 7y + 3 equal to 2 [B]7y + 3 = 2[/B]
The sum of 9 and victors age is 55
The sum of 9 and victors age is 55 Let v be Victor's age. We have the algebraic expression: [B]v + 9 = 55 [/B] If you want to solve or v, use our [URL='http://www.mathcelebrity.com/1unk.php?num=v%2B9%3D55&pl=Solve']equation calculator[/URL].
the sum of a number and its reciprocal is 5/2
the sum of a number and its reciprocal is 5/2 The phrase [I]a number[/I] means an arbitrary variable, let's call it x. The reciprocal of the number means 1/x. The sum means we add them: x + 1/x The word [I]is[/I] means an equation, so we set x + 1/x equal to 52 [B]x + 1/x = 52[/B]
The sum of a number and its reciprocal is 72
The sum of a number and its reciprocal is 72 The phrase [I]a number[/I] means an arbitrary variable, let's call it x x The reciprocal of the number is written as: 1/x The sum of a number and its reciprocal means we add: x + 1/x The word [I]is[/I] means an equation, so we set x + 1/x equal to 72 [B]x + 1/x = 72[/B]
The sum of a number and its reciprocal is five.
The sum of a number and its reciprocal is five. The phrase [I]a number[/I] means an arbitrary variable. Let's call it x. The reciprocal of the number is 1/x. The sum means we add them together: x + 1/x The word [I]is[/I] means an equation, so we set x + 1/x equal to 5 [B]x + 1/x = 5[/B]
The sum of a number and its square is 72. find the numbers?
The sum of a number and its square is 72. find the numbers? Let the number be n. We have: n^2 + n = 72 Subtract 72 from each side: n^2 + n - 72 = 0 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=n%5E2%2Bn-72%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic calculator[/URL], we have: [B]n = 8 or n = -9 [/B] Since the numbers do not state positive or negative, these are the two solutions.
the sum of a number and itself is 8
A number means an arbitrary variable, let's call it x. The sum of a number and itself means adding the number to itself x + x Simplified, we have 2x The word is means equal to, so we have an algebraic expression of: [B]2x= 8 [/B] IF you need to solve this equation, divide each side by 2 [B]x = 4[/B]
the sum of a number divided by 8 and 3 equals 6
"A Number" means an arbitrary variable, let's call it x. x divide d by 8 is written as a quotient x/8 The sum of x/8 and 3 means we add: x/8 + 3 Finally, equals means we have an equation, so we set our expression above equal to 6 x/8 + 3 = 6
the sum of doubling a number and 100 which totals to 160
the sum of doubling a number and 100 which totals to 160 Take this algebraic expression in pieces: [LIST=1] [*]Let the number be n. [*]Double it, means we multiply n by 2: 2n [*]The sum of this and 100 means we add 100 to 2n: 2n + 100 [*]The phrase [I]which totals[/I] means we set 2n + 100 equal to 160 [/LIST] [B]2n + 100 = 160[/B] <-- This is our algebraic expression If the question asks you to solve for n, then we [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B100%3D160&pl=Solve']type this equation into our search engine[/URL] and we get: [B]n = 30[/B]
The sum of five and twice a number is 17
The sum of five and twice a number is 17 [U]The phrase a number means an arbitrary variable, let's call it x[/U] x [U]Twice a number means we multiply x by 2:[/U] 2x [U]The sum of five and twice a number means we add 5 to 2x:[/U] 2x + 5 [U]The phrase [I]is[/I] means an equation, so we set 2x + 5 equal to 17 to get our algebraic expression[/U] [B]2x + 5 = 17[/B] [B][/B] As a bonus, if the problem asks you to solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=2x%2B5%3D17&pl=Solve']type in this algebraic expression into our math engine[/URL] and we get: x = 6
The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age
The sum of Jocelyn and Joseph's age is 40. In 5 years, Joseph will be twice as Jocelyn's present age. How old are they now? Let Jocelyn's age be a Let Joseph's age be b. We're given two equations: [LIST=1] [*]a + b = 40 [*]2(a + 5) = b + 5 [/LIST] We rearrange equation (1) in terms of a to get: [LIST=1] [*]a = 40 - b [*]2a = b + 5 [/LIST] Substitute equation (1) into equation (2) for a: 2(40 - b) = b + 5 80 - 2b = b + 5 To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=80-2b%3Db%2B5&pl=Solve']type it in our search engine[/URL] and we get: [B]b (Joseph's age) = 25[/B] Now, substitute b = 25 into equation (1) to solve for a: a = 40 - 25 [B]a (Jocelyn's age) = 15[/B]
The sum of Juan�s age and Sara�s age is 33 yrs. If Sara is 15 yrs old, how old is Juan?
The sum of Juan�s age and Sara�s age is 33 yrs. If Sara is 15 yrs old, how old is Juan? Let j be Juan's age and s be Sara's age. We have the following equations: [LIST=1] [*]j + s = 33 [*]s = 15 [/LIST] Substitute (2) into (1) j + 15 = 33 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=j%2B15%3D33&pl=Solve']equation solver[/URL], we get[B] j = 18[/B]
The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages?
The sum of Mr. Adams and Mrs. Benson's age is 55. The difference is 3. What are their ages? [U]Givens[/U] [LIST] [*]Let Mr. Adam's age be a [*]Let Mrs. Benson's age be b [*]We're given two equations where [I]sum[/I] means we add and [I]difference[/I] means we subtract: [/LIST] [LIST=1] [*]a + b = 55 [*]a - b = 3 [/LIST] Since we have opposite coefficients for b, we can take a shortcut and add equation 1 to equation 2: (a + a) + (b - b) = 55 + 3 Combining like terms and simplifying, we get: 2a = 58 To solve this equation for a, we [URL='https://www.mathcelebrity.com/1unk.php?num=2a%3D58&pl=Solve']type it in our search engine[/URL] and we get: a = [B]29[/B]
the sum of n and twice n is 12
Twice n means we multiply n by 2 2n The sum of n and twice n means we add n + 2n The word [I]is[/I] means equal to, so we set that expression above equal to 12 n + 2n = 12 Combine like terms: 3n = 12 Divide each side of the equation by 3 to isolate n n = 4 Check our work Twice n is 2*4 = 8 Add that to n = 4 8 + 4 12
The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. Ho
The sum of the ages of levi and renee is 89 years. 7 years ago levi's age was 4 times renees age. How old is Levi now? Let Levi's current age be l. Let Renee's current age be r. Were given two equations: [LIST=1] [*]l + r = 89 [*]l - 7 = 4(r - 7) [/LIST] Simplify equation 2 by multiplying through: [LIST=1] [*]l + r = 89 [*]l - 7 = 4r - 28 [/LIST] Rearrange equation 1 to solve for r and isolate l by subtracting l from each side: [LIST=1] [*]r = 89 - l [*]l - 7 = 4r - 28 [/LIST] Now substitute equation (1) into equation (2): l - 7 = 4(89 - l) - 28 l - 7 = 356 - 4l - 28 l - 7 = 328 - 4l To solve for l, we [URL='https://www.mathcelebrity.com/1unk.php?num=l-7%3D328-4l&pl=Solve']type the equation into our search engine[/URL] and we get: l = [B]67[/B]
The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times
The sum of the digits of a 2 digit number is 10. The value of the number is four more than 15 times the unit digit. Find the number. Let the digits be (x)(y) where t is the tens digit, and o is the ones digit. We're given: [LIST=1] [*]x + y = 10 [*]10x+ y = 15y + 4 [/LIST] Simplifying Equation (2) by subtracting y from each side, we get: 10x = 14y + 4 Rearranging equation (1), we get: x = 10 - y Substitute this into simplified equation (2): 10(10 - y) = 14y + 4 100 - 10y = 14y + 4 [URL='https://www.mathcelebrity.com/1unk.php?num=100-10y%3D14y%2B4&pl=Solve']Typing this equation into our search engine[/URL], we get: y = 4 Plug this into rearranged equation (1), we get: x = 10 - 4 x = 6 So our number xy is [B]64[/B]. Let's check our work against equation (1): 6 + 4 ? 10 10 = 10 Let's check our work against equation (2): 10(6)+ 4 ? 15(4) + 4 60 + 4 ? 60 + 4 64 = 64
The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number
The sum of the digits of a certain two-digit number is 16. Reversing its digits increases the number by 18. What is the number? Let x and (16-x) represent the original ten and units digits respectively Reversing its digits increases the number by 18 Set up the relational equation [10x + (16-x)] + 18 = 10(16 - x) + x Solving for x 9x + 34 = 160 - 9x Combine like terms 18x = 126 Divide each side of the equation by 18 18x/18 = 126/18 x = 7 So 16 - x = 16 - 7 = 9 The first number is 79, the other number is 97. and 97 - 79 = 18 so we match up. The number in our answer is [B]79[/B]
The sum of the squares of two consecutive positive integers is 61. Find these two numbers.
The sum of the squares of two consecutive positive integers is 61. Find these two numbers. Let the 2 consecutive integers be x and x + 1. We have: x^2 + (x + 1)^2 = 61 Simplify: x^2 + x^2 + 2x + 1 = 61 2x^2 + 2x + 1 = 61 Subtract 61 from each side: 2x^2 + 2x - 60 = 0 Divide each side by 2 x^2 + x - 30 Using our [URL='http://www.mathcelebrity.com/quadratic.php?num=x%5E2%2Bx-30&pl=Solve+Quadratic+Equation&hintnum=+0']quadratic equation calculator[/URL], we get: x = 5 and x = -6 The question asks for [I]positive integers[/I], so we use [B]x = 5. [/B]This means the other number is [B]6[/B].
The sum of three consecutive integers is 42
Let the 3 integers be x, y, and z. y = x + 1 z = y + 1, or x + 2. Set up our equation: x + (x + 1) + (x + 2) = 42 Group our variables and constants: (x + x + x) + (1 + 2) = 42 3x + 3 = 42 Subtract 3 from each side: 3x = 39 Divide each side of the equation by 3: [B]x = 13 So y = x + 1 = 14 z = x + 2 = 15 (x,y,z) = (13,14,15)[/B]
The sum of three numbers is 171. The second number is 1/2 of the first and the third is 3/4 of the f
The sum of three numbers is 171. The second number is 1/2 of the first and the third is 3/4 of the first. Find the numbers. We have three numbers, x, y, and z. [LIST=1] [*]x + y + z = 171 [*]y = 1/2x [*]z = 3/4x [/LIST] Substitute (2) and (3) into (1) x + 1/2x + 3/4x = 171 Use a common denominator of 4 for each x term 4x/4 + 2x/4 + 3x/4 = 171 (4 + 2 + 3)x/4 = 171 9x/4 = 171 [URL='https://www.mathcelebrity.com/prop.php?num1=9x&num2=171&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Plug this equation into our search engine[/URL], and we get [B]x = 76[/B] So y = 1/2(76) --> [B]y = 38[/B] Then z = 3/4(76) --> [B]z = 57[/B]
The Sum of three times a number and 18 is -39. Find the number
The Sum of three times a number and 18 is -39. Find the number. A number means an arbitrary variable, let us call it x. Three times x: 3x The sum of this and 18: 3x + 18 Is means equal to, so we set 3x + 18 = -39 3x + 18 = -39 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3x%2B18%3D-39&pl=Solve']equation solver[/URL], we get [B]x = -19[/B]
The sum of twice an integer and 3 times the next consecutive integer is 48
The sum of twice an integer and 3 times the next consecutive integer is 48 Let the first integer be n This means the next consecutive integer is n + 1 Twice an integer means we multiply n by 2: 2n 3 times the next consecutive integer means we multiply (n + 1) by 3 3(n + 1) The sum of these is: 2n + 3(n + 1) The word [I]is[/I] means equal to, so we set 2n + 3(n + 1) equal to 48: 2n + 3(n + 1) = 48 Solve for [I]n[/I] in the equation 2n + 3(n + 1) = 48 We first need to simplify the expression removing parentheses Simplify 3(n + 1): Distribute the 3 to each term in (n+1) 3 * n = (3 * 1)n = 3n 3 * 1 = (3 * 1) = 3 Our Total expanded term is 3n + 3 Our updated term to work with is 2n + 3n + 3 = 48 We first need to simplify the expression removing parentheses Our updated term to work with is 2n + 3n + 3 = 48 [SIZE=5][B]Step 1: Group the n terms on the left hand side:[/B][/SIZE] (2 + 3)n = 5n [SIZE=5][B]Step 2: Form modified equation[/B][/SIZE] 5n + 3 = + 48 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 3 and 48. To do that, we subtract 3 from both sides 5n + 3 - 3 = 48 - 3 [SIZE=5][B]Step 4: Cancel 3 on the left side:[/B][/SIZE] 5n = 45 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5n/5 = 45/5 Cancel the 5's on the left side and we get: n = [B]9[/B]
The sum of two consecutive integers plus 18 is 123
The sum of two consecutive integers plus 18 is 123. Let our first integer be n and our next integer be n + 1. We have: n + (n + 1) + 18 = 123 Group like terms to get our algebraic expression: 2n + 19 = 123 If we want to solve the algebraic expression using our [URL='http://www.mathcelebrity.com/1unk.php?num=2n%2B19%3D123&pl=Solve']equation solver[/URL], we get n = 52. This means the next integer is 52 + 1 = 53
The sum of two-fifths and f is one-half.
The sum of two-fifths and f is one-half. We write two-fifths as 2/5. The sum of two-fifths and f is written by adding f to two-fifths using the + sign: 2/5 + f one-half is written as 1/2 The word [I]is[/I] means equals, so we set up an equation where 2/5 + f equal to 1/2 [B]2/5 + f = 1/2[/B]
The sum of x and twice y is equal to m.
The sum of x and twice y is equal to m. Twice y means we multiply y by 2: 2y The sum of x and twice y: x + 2y The phrase [I]is equal to[/I] means an equation, so we set x + 2y equal to m [B]x + 2y = m[/B]
The team A scored 13 more points than Team B. The total of their score was 47. How many points did t
The team A scored 13 more points than Team B. The total of their score was 47. How many points did team A score? Let a be the amount of points A scored, and b be the amount of points B scored. We're given: [LIST=1] [*]a = b + 13 [*]a + b = 47 [/LIST] Plug (1) into (2) (b + 13) + b = 47 Combine like terms: 2b + 13 = 47 [URL='https://www.mathcelebrity.com/1unk.php?num=2b%2B13%3D47&pl=Solve']Typing this equation into our search engine[/URL], we get: b = 17 Now plug this into (1): a = 17 + 13 a = [B]30[/B]
The top part of the tree is 3 times as long as the trunk which equation can tulia use to find t the
The top part of the tree is 3 times as long as the trunk which equation can tulia use to find t the length of the trunk Let p be the top part of the tree. We have p = 3t. Divide by 3, we get t = [B]p/3[/B]
The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. h
The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins? Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given: [LIST=1] [*]a + h + c = 48 [*]a = 0.5h [*]a = c + 4 [/LIST] To isolate equations in terms of Suresh's age (a), let's do the following: [LIST] [*]Rewriting (3) by subtracting 4 from each side, we get c = a - 4 [*]Rewriting (2) by multiply each side by 2, we have h = 2a [/LIST] We have a new system of equations: [LIST=1] [*]a + h + c = 48 [*]h = 2a [*]c = a - 4 [/LIST] Plug (2) and (3) into (1) a + (2a) + (a - 4) = 48 Group like terms: (1 + 2 + 1)a - 4 = 48 4a - 4 = 48 [URL='https://www.mathcelebrity.com/1unk.php?num=4a-4%3D48&pl=Solve']Typing this equation into our search engine[/URL], we get: [B]a = 13 [/B]<-- Suresh's age This means that Hakima's age, from modified equation (2) above is: h = 2(13) [B]h = 26[/B] <-- Hakima's age This means that Saad's age, from modified equation (3) above is: c = 13 - 4 [B]c = 9[/B] <-- Saad's age [B] [/B]
The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your
The total cost for 9 bracelets, including shipping was $72. The shipping charge was $9. Define your variable and write an equation that models the cost of each bracelet. We set up a cost function as fixed cost plus total cost. Fixed cost is the shipping charge of $9. So we have the following cost function where n is the cost of the bracelets: C(b) = nb + 9 We are given C(9) = 72 and b = 9 9n + 9 = 72 [URL='https://www.mathcelebrity.com/1unk.php?num=9n%2B9%3D72&pl=Solve']Run this through our equation calculator[/URL], and we get [B]n = 7[/B].
The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hour
The total cost to fix your bike is $45 the parts cost $10 and the labor cost seven dollars per hour how many hours were there: Set up a cost function where h is the number of hours: 7h + 10 = 45 To solve for h, we t[URL='https://www.mathcelebrity.com/1unk.php?num=7h%2B10%3D45&pl=Solve']ype this equation into our search engine[/URL] and we get: h = [B]5[/B]
The value of a company van is $15,000 and decreased at a rate of 4% each year. Approximate how much
The value of a company van is $15,000 and decreased at a rate of 4% each year. Approximate how much the van will be worth in 7 years. Each year, the van is worth 100% - 4% = 96%, or 0.96. We have the Book value equation: B(t) = 15000(0.96)^t where t is the time in years from now. The problem asks for B(7): B(7) = 15000(0.96)^7 B(7) = 15000(0.7514474781) B(7) = [B]11,271.71[/B]
The value of a stock begins at $0.07 and increases by $0.02 each month. Enter an equation representi
The value of a stock begins at $0.07 and increases by $0.02 each month. Enter an equation representing the value of the stock v in any month m. Set up our equation v(m): [B]v(m) = 0.07 + 0.02m[/B]
The value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters
The value of all the quarters and dimes in a parking meter is $18. There are twice as many quarters as dimes. What is the total number of dimes in the parking meter? Let q be the number of quarters. Let d be the number of dimes. We're given: [LIST=1] [*]q = 2d [*]0.10d + 0.25q = 18 [/LIST] Substitute (1) into (2): 0.10d + 0.25(2d) = 18 0.10d + 0.5d = 18 [URL='https://www.mathcelebrity.com/1unk.php?num=0.10d%2B0.5d%3D18&pl=Solve']Type this equation into our search engine[/URL], and we get [B]d = 30[/B].
The volleyball team and the wrestling team at Clarksville High School are having a joint car wash t
The volleyball team and the wrestling team at Clarksville High School are having a joint car wash today, and they are splitting the revenues. The volleyball team gets $4 per car. In addition, they have already brought in $81 from past fundraisers. The wrestling team has raised $85 in the past, and they are making $2 per car today. After washing a certain number of cars together, each team will have raised the same amount in total. What will that total be? How many cars will that take? Set up the earnings equation for the volleyball team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 4w + 81 Set up the earnings equation for the wrestling team where w is the number of cars washed: E = Price per cars washed * w + past fundraisers E = 2w + 85 If the raised the same amount in total, set both earnings equations equal to each other: 4w + 81 = 2w + 85 Solve for [I]w[/I] in the equation 4w + 81 = 2w + 85 [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4w and 2w. To do that, we subtract 2w from both sides 4w + 81 - 2w = 2w + 85 - 2w [SIZE=5][B]Step 2: Cancel 2w on the right side:[/B][/SIZE] 2w + 81 = 85 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 81 and 85. To do that, we subtract 81 from both sides 2w + 81 - 81 = 85 - 81 [SIZE=5][B]Step 4: Cancel 81 on the left side:[/B][/SIZE] 2w = 4 [SIZE=5][B]Step 5: Divide each side of the equation by 2[/B][/SIZE] 2w/2 = 4/2 w = [B]2 <-- How many cars it will take [/B] To get the total earnings, we take either the volleyball or wrestling team's Earnings equation and plug in w = 2: E = 4(2) + 81 E = 8 + 81 E = [B]89 <-- Total Earnings[/B]
there are $4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coins
there are $4.20 in nickel and quarters. There are 6 more nickels than quarters there. How many coins of each are there We're given two equations: [LIST=1] [*]n = q + 6 [*]0.05n + 0.25q = 4.2 [/LIST] Substitute equation (1) into equation (2): 0.05(q + 6) + 0.25q = 4.2 Multiply through and simplify: 0.05q + 0.3 + 0.25q 0.3q + 0.3 = 4.2 To solve for q, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.3q%2B0.3%3D4.2&pl=Solve']type this equation into the search engine[/URL] and we get: q = [B]13 [/B] To solve for n, we plug in q = 13 into equation (1): n = 13 + 6 n = [B]19[/B]
there are 120 calories in 3/4 cup serving of cereal. How many Calories are there in 6 cups of cereal
120/3/4 = x/6 Cross multiply: 0.75x = 720 Divide each side of the equation by 0.75 [B]x = 960[/B]
There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How
There are 13 animals in the barn. some are chickens and some are pigs. there are 40 legs in all. How many of each animal are there? Chickens have 2 legs, pigs have 4 legs. Let c be the number of chickens and p be the number of pigs. Set up our givens: (1) c + p = 13 (2) 2c + 4p = 40 [U]Rearrange (1) to solve for c by subtracting p from both sides:[/U] (3) c = 13 - p [U]Substitute (3) into (2)[/U] 2(13 - p) + 4p = 40 26 - 2p + 4p = 40 [U]Combine p terms[/U] 2p + 26 = 40 [U]Subtract 26 from each side:[/U] 2p = 14 [U]Divide each side by 2[/U] [B]p = 7[/B] [U]Substitute p = 7 into (3)[/U] c = 13 - 7 [B]c = 6[/B] For a shortcut, you could use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=c+%2B+p+%3D+13&term2=2c+%2B+4p+%3D+40&pl=Cramers+Method']simultaneous equations calculator[/URL]
There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults?
There are 144 people in an audience. The ratio of adults to children is 5 to 3. How many are adults? We set up an equation to represent this: 5x + 3x = 144 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B3x%3D144&pl=Solve']Typing this equation into our search engine[/URL], we get: x = 18 This means we have: Adults = 5(18) [B]Adults = 90[/B] Children = 3(18) [B]Children = 54[/B]
There are 320 pupils there are 24 more girls than boys how many boys are there
Let b = boys and g = girls. We have two equations: (1) b + g = 320 (2) g = b + 24 Substitute (2) into (1) for g b + (b + 24) = 320 Combine b terms: 2b + 24 = 320 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=2b%2B24%3D320&pl=Solve']equation calculator[/URL]: [B]b = 148 [/B] Substitute b = 148 into (2) g = 148 + 24 [B]g = 172[/B]
There are 33 students in an Algebra I class. There are 7 fewer girls than boys. How many girls are i
There are 33 students in an Algebra I class. There are 7 fewer girls than boys. How many girls are in the class? Let b be the number of boys and g be the number of girls. We are given 2 equations: [LIST=1] [*]g = b - 7 [*]b + g = 33 [/LIST] Substitute (1) into (2): b + (b - 7) = 33 Combine like terms: 2b - 7 = 33 [URL='https://www.mathcelebrity.com/1unk.php?num=2b-7%3D33&pl=Solve']Typing this equation into our search engine[/URL], we get b = 20. Since the problem asks for how many girls (g) we have, we substitute b = 20 into Equation (1): g = 20 - 7 [B]g = 13[/B]
There are 63 students in middle school chorus. There are 11 more boys than girls. How many boys x an
There are 63 students in middle school chorus. There are 11 more boys than girls. How many boys x and girls y are in the chorus? Set up equations: [LIST=1] [*]x + y = 63 [*]x = y + 11 [/LIST] Substitute (1) into (2) y + 11 + y = 63 2y + 11 = 63 Use our [URL='http://www.mathcelebrity.com/1unk.php?num=2y%2B11%3D63&pl=Solve']equation solver[/URL]: [B]y = 26[/B]
There are 64 members in the history club. 11 less than half of the members are girls. How many membe
There are 64 members in the history club. 11 less than half of the members are girls. How many members are boys? Set up two equations where b = the number of boys and g = the number of girls [LIST=1] [*]b + g = 64 [*]1/2(b + g) - 11 = g [/LIST] Substitute (1) for b + g into (2) 1/2(64) - 11 = g 32 - 11 = g [B]g = 21[/B] Substitute g = 21 into (1) b + 21 = 64 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=b%2B21%3D64&pl=Solve']equation calculator[/URL], we get: [B]b = 43[/B]
There are 85 students in a class, 40 of them like math,31 of them like science, 12 of them like both
There are 85 students in a class, 40 of them like math,31 of them like science, 12 of them like both, how many don't like either. We have the following equation: Total Students = Students who like math + students who like science - students who like both + students who don't like neither. Plug in our knowns, we get: 85 = 40 + 31 - 12 + Students who don't like neither 85 = 59 + Students who don't like neither Subtract 59 from each side, we get: Students who don't like neither = 85 - 59 Students who don't like neither = [B]26[/B]
There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The
There are two numbers. The sum of 4 times the first number and 3 times the second number is 24. The difference between 2 times the first number and 3 times the second number is 24. Find the two numbers. Let the first number be x and the second number be y. We have 2 equations: [LIST=1] [*]4x + 3y = 24 [*]2x - 3y = 24 [/LIST] Without doing anything else, we can add the 2 equations together to eliminate the y term: (4x + 2x) + (3y - 3y) = (24 + 24) 6x = 48 Divide each side by 6: [B]x = 8 [/B] Substitute this into equation (1) 4(8) + 3y = 24 32 + 3y = 24 [URL='https://www.mathcelebrity.com/1unk.php?num=32%2B3y%3D24&pl=Solve']Type 32 + 3y = 24 into our search engine[/URL] and we get [B]y = 2.6667[/B].
There is a sales tax of $4 on an item that cost $54 before tax. The sales tax on a second item is $1
There is a sales tax of $4 on an item that cost $54 before tax. The sales tax on a second item is $14. How much does the second item cost before tax? Sales Tax on First Item = Tax Amount / Before Tax Sale Amount Sales Tax on First Item = 4/54 Sales Tax on First Item = 0.07407407407 For the second item, let the before tax sale amount be b. We have: 0.07407407407b = 14 To solve this equation for b, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.07407407407b%3D14&pl=Solve']type it in our search engine[/URL] and we get: b = [B]189[/B]
There were 150 students at a dance. There were 16 more boys than girls. How many boys were there?
Set up two equations: (1) b = g + 16 (2) b + g = 150 Substitute equation (1) into (2) (g + 16) + g = 150 Combine like terms 2g + 16 = 150 Subtract 16 from each side 2g = 134 Divide each side by 2 to isolate g g = 67 Substitute this into equation (1) b = 67 + 16 [B]b = 83[/B]
There were 175 tickets sold for the upcoming event in the gym. If students tickets cost $5 and adult
There were 175 tickets sold for the upcoming event in the gym. If students tickets cost $5 and adult tickets are $8, tell me how many tickets were sold if gate receipts totaled $1028? Let s be the number of student tickets and a be the number of adult tickets. We are given: a + s = 175 8a + 5s = 1028 There are 3 ways to solve this, all of which give us: [B]a = 51 s = 124 [/B] [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Substitution']Substitution Method[/URL] [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Elimination']Elimination Method[/URL] [URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=a+%2B+s+%3D+175&term2=8a+%2B+5s+%3D+1028&pl=Cramers+Method']Cramers Method[/URL]
Thin Lens Distance
Given two out of three items in the thin lens equation, this solves for the third.
Tickets for a concert were priced at $8 for students and $10 for nonstudents. There were 1340 ticket
Tickets for a concert were priced at $8 for students and $10 for nonstudents. There were 1340 tickets sold for a total of $12,200. How many student tickets were sold? Let s be the number of student tickets and n be the number of nonstudent tickets: [LIST=1] [*]n + s = 1340 [*]10n + 8s = 12200 [/LIST] Use our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=n+%2B+s+%3D+1340&term2=10n+%2B+8s+%3D+12200&pl=Cramers+Method']simultaneous equation calculator[/URL]: n = 740 [B]s = 600[/B]
Time and Distance
Let h be the number of hours that pass when Charlie starts. We have the following equations: [LIST] [*]Charlie: D = 40h + 9 [*]Danny: D = 55h [/LIST] Set them equal to each other: 40h + 9 = 55h Subtract 40h from both sides: 15h = 9 h = 3/5 [B]3/5 of an hour = 3(60)/5 = 36 minutes[/B]
Time and Distance
Thank you so much [QUOTE="math_celebrity, post: 1003, member: 1"]Let h be the number of hours that pass when Charlie starts. We have the following equations: [LIST] [*]Charlie: D = 40h + 9 [*]Danny: D = 55h [/LIST] Set them equal to each other: 40h + 9 = 55h Subtract 40h from both sides: 15h = 9 h = 3/5 [B]3/5 of an hour = 3(60)/5 = 36 minutes[/B][/QUOTE]
Tina's mom made brownies. When tinas friend came over they ate 1/3 of the brownies. Her sister ate 2
Tina's mom made brownies. When tinas friend came over they ate 1/3 of the brownies. Her sister ate 2 and her dad ate 4. If there are 26 brownies left. How many did her mom make Let b denote the number of brownies Tina's mom made. We're given: b - 1/3b - 2 - 4 = 26 Combining like terms, we have: 2b/3 - 6 = 26 Add 6 to each side, we get: 2b/3 = 32 To solve this equation for b, we [URL='https://www.mathcelebrity.com/prop.php?num1=2b&num2=32&den1=3&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']type it in our math engine[/URL] and we get: b = [B]48[/B]
To be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a total
To be a member of world fitness gym, it costs $60 flat fee and $30 per month. Maria has paid a total of $210 for her gym membership so far. How long has Maria been a member to the gym? The cost function C(m) where m is the number of months for the gym membership is: C(m) = 30m + 60 We're given that C(m) = 210 for Maria. We want to know the number of months (m) that Maria has been a member. With C(m) = 210, we have: 30m + 60 =210 To solve this equation, [URL='https://www.mathcelebrity.com/1unk.php?num=30m%2B60%3D210&pl=Solve']we type it in our search engine[/URL] and we get: m = [B]5[/B]
To convert from Celsius to Fahrenheit, multiply by 1.8 and add 32. Write a formula to describe this
To convert from Celsius to Fahrenheit, multiply by 1.8 and add 32. Write a formula to describe this relationship. Given C as Celsius and F as Fahrenheit, we have the following equation: [B]F = 1.8C + 32[/B]
To make an international telephone call, you need the code for the country you are calling. The code
To make an international telephone call, you need the code for the country you are calling. The code for country A, country B, and C are three consecutive integers whose sum is 90. Find the code for each country. If they are three consecutive integers, then we have: [LIST=1] [*]B = A + 1 [*]C = B + 1, which means C = A + 2 [*]A + B + C = 90 [/LIST] Substitute (1) and (2) into (3) A + (A + 1) + (A + 2) = 90 Combine like terms 3A + 3 = 90 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=3a%2B3%3D90&pl=Solve']equation calculator[/URL], we get: [B]A = 29[/B] Which means: [LIST] [*]B = A + 1 [*]B = 29 + 1 [*][B]B = 30[/B] [*]C = A + 2 [*]C = 29 + 2 [*][B]C = 31[/B] [/LIST] So we have [B](A, B, C) = (29, 30, 31)[/B]
To rent a building for a school dance, Ava paid 120 plus 2.50 for each student. To attend the school
To rent a building for a school dance, Ava paid 120 plus 2.50 for each student. To attend the school all together Ava paid 325. How many students attended the dance? Let the number of students be s. We're given 2.50s + 120 = 325 [URL='https://www.mathcelebrity.com/1unk.php?num=2.50s%2B120%3D325&pl=Solve']Type this equation into our search engine[/URL], and we get: s = [B]82[/B]
To rent a car it costs $12 per day and $0.50 per kilometer traveled. If a car were rented for 5 days
To rent a car it costs $12 per day and $0.50 per kilometer traveled. If a car were rented for 5 days and the charge was $110.00, how many kilometers was the car driven? Using days as d and kilometers as k, we have our cost equation: Rental Charge = $12d + 0.5k We're given Rental Charge = 110 and d = 5, so we plug this in: 110 = 12(5) + 0.5k 110 = 60 + 0.5k [URL='https://www.mathcelebrity.com/1unk.php?num=60%2B0.5k%3D110&pl=Solve']Plugging this into our equation calculator[/URL], we get: [B]k = 100[/B]
To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional po
To ship a package with UPS, the cost will be $7 for the first pound and $0.20 for each additional pound. To ship a package with FedEx, the cost will be $5 for the first pound and $0.30 for each additional pound. How many pounds will it take for UPS and FedEx to cost the same? If you needed to ship a package that weighs 8 lbs, which shipping company would you choose and how much would you pay? [U]UPS: Set up the cost function C(p) where p is the number of pounds:[/U] C(p) = Number of pounds over 1 * cost per pounds + first pound C(p) = 0.2(p - 1) + 7 [U]FedEx: Set up the cost function C(p) where p is the number of pounds:[/U] C(p) = Number of pounds over 1 * cost per pounds + first pound C(p) = 0.3(p - 1) + 5 [U]When will the costs equal each other? Set the cost functions equal to each other:[/U] 0.2(p - 1) + 7 = 0.3(p - 1) + 5 0.2p - 0.2 + 7 = 0.3p - 0.3 + 5 0.2p + 6.8 = 0.3p + 4.7 To solve this equation for p, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.2p%2B6.8%3D0.3p%2B4.7&pl=Solve']type it in our search engine[/URL] and we get: p = [B]21 So at 21 pounds, both UPS and FedEx costs are equal [/B] Now, find out which shipping company has a better rate at 8 pounds: [U]UPS:[/U] C(8) = 0.2(8 - 1) + 7 C(8) = 0.2(7) + 7 C(8) = 1.4 + 7 C(8) = 8.4 [U]FedEx:[/U] C(8) = 0.3(8 - 1) + 5 C(8) = 0.3(7) + 5 C(8) = 2.1 + 5 C(8) = [B]7.1[/B] [B]Therefore, FedEx is the better cost at 8 pounds since the cost is lower[/B] [B][/B]
Tom has a collection 21 CDs and Nita has a collection of 14 CDs. Tom is adding 3 cds a month to his
Tom has a collection 21 CDs and Nita has a collection of 14 CDs. Tom is adding 3 cds a month to his collection while Nita is adding 4 CDs a month to her collection. Find the number of months after which they will have the same number of CDs? Set up growth equations for the CDs where c = number of cds after m months Tom: c = 21 + 3m Nita: c = 14 + 4m Set the c equations equal to each other 21 + 3m = 14 + 4m Using our [URL='http://www.mathcelebrity.com/1unk.php?num=21%2B3m%3D14%2B4m&pl=Solve']equation calculator[/URL], we get [B]m = 7[/B]
Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtra
Tom is 2 years older than Sue and Bill is twice as old as Tom. If you add all their ages and subtract 2, the sum is 20. How old is Bill? Let t be Tom's age., s be Sue's age, and b be Bill's age. We have the following equations: [LIST=1] [*]t = s + 2 [*]b = 2t [*]s + t + b - 2 = 20 [/LIST] Get (2) in terms of s (2) b = 2(s + 2) <-- using (1), substitute for t So we have (3) rewritten with substitution as: s + (s + 2) + 2(s + 2) - 2 = 20 s + (s + 2) + 2s + 4 - 2 = 20 Group like terms: (s + s + 2s) + (2 + 4 - 2) = 20 4s + 4 = 20 Run this through our [URL='https://www.mathcelebrity.com/1unk.php?num=4s%2B4%3D20&pl=Solve']equation calculator [/URL]to get s = 4 Above, we had b = 2(s + 2) Substituting s = 4, we get: 2(4 + 2) = 2(6) = [B]12 Bill is 12 years old[/B]
Tom�s is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount
Tom�s is a salesperson who earns a monthly salary of $2250 plus a 3% commission on the total amount of his sales. What were his sales last month if he earned a total of $4500? Let total sales be s. We're given the following earnings equation: 0.03s + 2250 = 4500 To solve for s, we [URL='https://www.mathcelebrity.com/1unk.php?num=0.03s%2B2250%3D4500&pl=Solve']type this equation into our search engine[/URL] and we get: s = [B]75,000[/B]
Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to
Translate this sentence into an equation. 43 is the sum of 17 and Gregs age. Use the variable g to represent Gregs age. The sum of 17 and Greg's age: g + 17 The word [I]is[/I] means equal to, so we set g + 17 equal to 43 [B]g + 17 = 43[/B] <-- This is our algebraic expression If you want to solve this equation for g, use our [URL='http://www.mathcelebrity.com/1unk.php?num=g%2B17%3D43&pl=Solve']equation calculator[/URL]. [B]g = 26[/B]
Translate this sentence into an equation. 48 is the difference of Ritas age and 11 . Use the variabl
Translate this sentence into an equation. 48 is the difference of Ritas age and 11 . Use the variable r to represent Ritas age. The difference of Rita's age and 11 is written: r - 11 The phrase [I]is[/I] means equal to, so we set r - 11 equal to 48 r - 11 = 48
Translate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variabl
Translate this sentence into an equation. 49 is the difference of Diegos age and 17. Use the variable d to represent Diegos age. The difference means we subtract, so we have d as Diego's age minus 17 d - 17 The word "is" means an equation, so we set d - 17 equal to 49 [B]d - 17 = 49[/B]
Translate this sentence into an equation. The difference of Maliks age and 15 is 63 Use the variable
Translate this sentence into an equation. The difference of Maliks age and 15 is 63 Use the variable m to represent Malik's age. [B]m - 15 = 63 [/B] To solve this equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=m-15%3D63&pl=Solve']equation calculator[/URL].
Trinomials
Checks to see if equations in the trinomial form ax2 + bx + c are a perfect square as well as completing the square from equations in the form ax2 + bx + ?. Also shows you a perfect square trinomial
triple the value of c plus 3 is 84
Triple the value of c means we multiply c by 3 3c Plus 3 means we add 3 3c + 3 Is, means equal to, so we set our expression equal to 84 [B]3c +3 = 84 [/B] If you want to solve that equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3c%2B3%3D84&pl=Solve']equation solver[/URL]: c = 27
True False Equations
Determines if a set of addition and subtraction of numbers on each side of an equation are equivalent. Also known as true or false equations
Trump stamps sold at $1.25 and Obama stamps sold at $2 . How many of each stamp was sold if 700 stam
Trump stamps sold at $1.25 and Obama stamps sold at $2 . How many of each stamp was sold if 700 stamps were sold making $1250 Let o be the number of Obama stamps. Let t be the number of Trump stamps. We have two equations: [LIST=1] [*]o + t = 700 [*]2o + 1.25t = 1250 [/LIST] Using our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=o%2Bt%3D700&term2=2o%2B1.25t%3D1250&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [B]o = 500 t = 200[/B]
Twice a first number decreased by a second number is 16. The first number increased by 3 times the s
Twice a first number decreased by a second number is 16. The first number increased by 3 times the second number is 1. Find the numbers. Let the first number be x and the second number be y. We're given: [LIST=1] [*]2x - y = 16 [*]x + 3y = 1 [/LIST] Using our simultaneous equations calculator, you can solve this 3 ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=2x+-+y+%3D+16&term2=x+%2B+3y+%3D+1&pl=Cramers+Method']Cramers Rule[/URL] [/LIST] No matter what method we use, we get the same answers: [B]x = 7 y = -2 (x, y) = (7, -2) [/B] Let's check our work in equation 1: 2(7) - -2 ? 16 14 + 2 ? 16 16 = 16 <-- Check Let's check our work in equation 2: 7 + 3(-2) ? 1 7 - 6 ? 1 1 = 1 <-- Check
twice the difference of a number and 3 is equal to 3 times the sum of a number and 2
twice the difference of a number and 3 is equal to 3 times the sum of a number and 2. We've got 2 algebraic expressions here. Let's take them in parts. Left side algebraic expression: twice the difference of a number and 3 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]The word [I]difference[/I] means we subtract 3 from the variable x [*]x - 3 [*]Twice this difference means we multiply (x - 3) by 2 [*]2(x - 3) [/LIST] Right side algebraic expression: 3 times the sum of a number and 2 [LIST] [*]The phrase [I]a number[/I] means an arbitrary variable, let's call it x. [*]The word [I]sum[/I] means we add 2 to the variable x [*]x + 2 [*]3 times the sum means we multiply (x + 2) by 3 [*]3(x + 2) [/LIST] Now, we have both algebraic expressions, the problem says [I]is equal to[/I] This means we have an equation, where we set the left side algebraic expression equal to the right side algebraic expression using the equal sign (=) to get our answer [B]2(x - 3) = 3(x + 2)[/B]
twice the difference of a number and 55 is equal to 3 times the sum of a number and 8
twice the difference of a number and 55 is equal to 3 times the sum of a number and 8 Take this algebraic expression in pieces. Left side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The difference of this number and 55 means we subtract 55 from x x - 55 Twice the difference means we multiply x - 55 by 2 2(x - 55) Right side: The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x The sum of a number and 8 means we add 8 to x x + 8 3 times the sum means we multiply x + 8 by 3 3(x + 8) Now that we have the left and right side of the expressions, we see the phrase [I]is equal to[/I]. This means an equation, so we set the left side equal to the right side: [B]2(x - 55) = 3(x + 8)[/B]
Two consecutive even integers that equal 126
Two consecutive even integers that equal 126 Let the first integer equal x. So the next even integer must be x + 2. The sum which is equal to 126 is written as x + (x + 2) = 126 Simplify: 2x + 2 = 126 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2x%2B2%3D126&pl=Solve']equation calculator,[/URL] we get: x = 62 This means the next consecutive even integer is 62 = 2 = 64. So our two even consecutive integers with a sum of 126 are [B](62, 64)[/B]
two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worke
two mechanics worked on a car. the first mechanic worked for 10 hours, and the second mechanic worked for 5 hours. together they charged a total of 1225. what was the rate charged per hour by each mechanic if the sum of the two rates was 170 per hour? Set up two equations: (1) 10x + 5y = 1225 (2) x + y = 170 Rearrange (2) x = 170 - y Substitute that into (1) 10(170 - y) + 5y = 1225 1700 - 10y + 5y = 1225 1700 - 5y = 1225 Move 5y to the other side 5y + 1225 = 1700 Subtract 1225 from each side 5y =475 Divide each side by 5 [B]y = 95[/B] Which means x = 170 - 95, [B]x = 75[/B]
Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked
Two mechanics worked on a car. the first mechanic worked for 5 hours snd the second mechanic worked for 15 hours. Together they charged a total of $2375. What was the rate charged per hour by each mechanic if the sum of the two rates was $235 per hour? Setup equations where x is the rate of the first mechanic and y is the rate of the second mechanic: [LIST] [*]5x + 15y = 2375 [*]x + y = 235 [/LIST] Using Cramers method with our [URL='http://www.mathcelebrity.com/simultaneous-equations.php?term1=5x+%2B+15y+%3D+2375&term2=x+%2B+y+%3D+235&pl=Cramers+Method']simultaneous equations calculator[/URL], we get: [LIST] [*][B]x = 115[/B] [*][B]y = 120[/B] [/LIST]
Two numbers that total 44 and have a difference of 6
Two numbers that total 44 and have a difference of 6. Let the two numbers be x and y. We're given the following equations: [LIST=1] [*]x + y = 44 <-- Total means a sum [*]x - y = 6 [/LIST] Add the two equations together: (x + x) + (y - y) = 44 + 6 Cancelling the y terms, we have: 2x = 50 [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D50&pl=Solve']Typing this equation into the search engine[/URL], we get: [B]x = 25 [/B] Rearranging equation (2) above, we get: y = x - 6 Substituting x = 25 into this, we get: y = 25 - 6 [B]y = 19[/B]
Two numbers total 12, and their differences is 20. Find the two numbers.
Two numbers total 12, and their differences is 20. Find the two numbers. Let the first number be x. Let the second number be y. We're given two equations: [LIST=1] [*]x + y = 12 [*]x - y = 20 [/LIST] Since we have y coefficients of (-1 and 1) that cancel, we add the two equations together: (x + x) + (y - y) = 12 + 20 The y terms cancel, so we have: 2x = 32 [URL='https://www.mathcelebrity.com/1unk.php?num=2x%3D32&pl=Solve']Type this equation into our search engine[/URL] and we get: x = [B]16[/B] Substitute this value of x = 16 back into equation 1: 16 + y = 12 [URL='https://www.mathcelebrity.com/1unk.php?num=16%2By%3D12&pl=Solve']Typing this equation into our search engine[/URL], we get: y = [B]-4 [/B] Now, let's check our work for both equations: [LIST=1] [*]16 - 4 = 12 [*]16 - -4 --> 16 + 4 = 20 [/LIST] So these both check out. (x, y) = ([B]16, -4)[/B]
Two numbers total 50 and have a difference of 28. Find the two numbers.
Two numbers total 50 and have a difference of 28. Find the two numbers. Using x and y as our two numbers, we write the following 2 equations: [LIST=1] [*]x + y = 50 [*]x - y = 28 [/LIST] Add the 2 rows: 2x = 78 Divide each side by 2: [B]x = 39[/B] If x = 39, then from (1), we have y = 50 - 39 [B]y = 11[/B]
Two numbers total 83 and have a difference of 17 find the two numbers
Let the numbers be x and y. Set up our givens: [LIST=1] [*]x + y = 83 [*]x - y = 17 [*]Rearrange (2), by adding y to each side, we have: x = 17 + y [/LIST] [U]Substitute (3) into (1):[/U] (17 + y) + y = 83 [U]Group y terms[/U] 2y + 17 = 83 [U]Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2y%2B17%3D83&pl=Solve']equation solver[/URL], we get:[/U] [B]y = 33 [/B] [U]Substitute that into (3)[/U] x = 17 + 33 [B]x = 50 [/B] So our two numbers (x, y) = (33, 50)
two pages that face each other in a book have a sum of 569
two pages that face each other in a book have a sum of 569 Pages that face each other are consecutive. Let the first page be p. The second page is p + 1. Their sum is: p + p + 1 = 569 [URL='https://www.mathcelebrity.com/1unk.php?num=p%2Bp%2B1%3D569&pl=Solve']Type this equation into our search engine to solve for p[/URL], and we get: p = 284 This means p + 1 = 284 + 1 = 285 So the pages that face each other having a sum of 569 are: [B]284, 285[/B]
Tyler has a meal account with $1200 in it to start the school year. Each week he spends $21 on food
Tyler has a meal account with $1200 in it to start the school year. Each week he spends $21 on food a.) write an equation that relates the amount in the account (a) with the number of (w) weeks b.) How many weeks will it take until Tyler runs out of money? [U]Part a) where w is the number of weeks[/U] a = Initial account value - weekly spend * w ([I]we subtract because Tyler spends)[/I] a = [B]1200 - 21w [/B] [U]Part b)[/U] We want to know the number of weeks it takes where a = 0. So we have: 1200 - 21w = 0 To solve for w, we [URL='https://www.mathcelebrity.com/1unk.php?num=1200-21w%3D0&pl=Solve']type this equation into our search engine[/URL] and we get: w = 57.14 weeks The problem asks for when he runs out of money, so we round up to [B]58 whole weeks[/B]
Tyrone re sells 3 pairs of Yeezys and a pair of Nikes for 250$. Nucci re sells a pair of Yeezys and
Tyrone re sells 3 pairs of Yeezys and a pair of Nikes for 250$. Nucci re sells a pair of Yeezys and Nikes for 150$ How much does a pair of Yeezys cost? Let y be the cost of Yeezy's and n be the cost of Nike's. We're given two equations: [LIST=1] [*]3y + n = 250 [*]y + n = 150 [/LIST] We have a system of equations, and we can solve it using one of three ways: [LIST] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3y+%2B+n+%3D+250&term2=y+%2B+n+%3D+150&pl=Substitution']Substitution Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3y+%2B+n+%3D+250&term2=y+%2B+n+%3D+150&pl=Elimination']Elimination Method[/URL] [*][URL='https://www.mathcelebrity.com/simultaneous-equations.php?term1=3y+%2B+n+%3D+250&term2=y+%2B+n+%3D+150&pl=Cramers+Method']Cramer's Rule[/URL] [/LIST] No matter what method we choose, we get: [LIST] [*][B]n = 100[/B] [*][B]y = 50[/B] [/LIST]
u=ak/b for a
Cross multiply: ub = ak Divide each side of the equation by k to isolate a: a = ub/k
Unknown Number
Determines the unknown number needed to make an equation true.
V ? E + F = 2 for e
V ? E + F = 2 for e To solve this literal equation, we want to isolate e. Add E to both sides: V ? E + F + E = 2 + E The E's cancel on the left side, so we have: V + F = 2 + E Subtract 2 from each side: V + F - 2 = 2 + E + 2 The 2's cancel on the right side, so we have: E = [B]V + F - 2[/B]
Variation Equations
This calculator solves the following direct variation equations and inverse variation equations below:
* y varies directly as x
* y varies inversely as x
* y varies directly as the square of x
* y varies directly as the cube of x
* y varies directly as the square root of x
* y varies inversely as the square of x
* y varies inversely as the cube of x
* y varies inversely as the square root of x
Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years.
Victoria is 4 years older than her neighbor. The sum of their ages is no more than 14 years. Let Victoria's age be v. And her neighbor's age be n. We're given: [LIST=1] [*]v = n + 4 [*]v + n <=14 <-- no more than means less than or equal to [/LIST] Substitute Equation (1) into Inequality (2): (n + 4) + n <= 14 Combine like terms: 2n + 4 <= 14 [URL='https://www.mathcelebrity.com/1unk.php?num=2n%2B4%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get: n <= 5 Substituting this into inequality (2): v + 5 <= 14 [URL='https://www.mathcelebrity.com/1unk.php?num=v%2B5%3C%3D14&pl=Solve']Typing this inequality into our search engine[/URL], we get: [B]v <= 9[/B]
Water flows from tank A to tank B at the rate of 2 litres per minute.
Water flows from tank A to tank B at the rate of 2 litres per minute. Initially tank A has 200 litres in it and tank B has 100 Litres in it. Water drains from tank B at 0.5 litres per minute. After how many minutes are there equal volumes of water in the 2 tanks? Write an equation and solve it.
Water flows from tank A to tank B at the rate of 2 litres per minute.
[QUOTE="Jahn, post: 78, member: 5"]Water flows from tank A to tank B at the rate of 2 litres per minute. Initially tank A has 200 litres in it and tank B has 100 Litres in it. Water drains from tank B at 0.5 litres per minute. After how many minutes are there equal volumes of water in the 2 tanks? Write an equation and solve it.[/QUOTE] Tank A: V = 200 - 2x Tank B: V = 100 - 0.5x Where x is the number of minutes passed. Set them equal to each other 200 - 2x = 100 - 0.5x Subtract 100 from each side: 100 - 2x = -0.5x Add 2x to each side: 1.5x = 100 Divide each side of the equation by x: x = 66.66666667
what integer is tripled when 9 is added to 3 fourths of it?
what integer is tripled when 9 is added to 3 fourths of it? Let the integer be n. Tripling an integer means multiplying it by 3. We're given: 3n = 3n/4 + 9 Since 3 = 12/4, we have: 12n/4 = 3n/4 + 9 Subtract 3n/4 from each side: 9n/4 = 9 [URL='https://www.mathcelebrity.com/prop.php?num1=9n&num2=9&den1=4&den2=1&propsign=%3D&pl=Calculate+missing+proportion+value']Typing this equation into the search engine[/URL], we get: [B]n = 4[/B]
What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.4%? Round
What is the annual nominal rate compounded daily for a bond that has an annual yield of 5.4%? Round to three decimal places. Use a 365 day year. [U]Set up the accumulation equation:[/U] (1+i)^365 = 1.054 [U]Take the natural log of each side[/U] 365 * Ln(1 + i) = 1.054 Ln(1 + i) = 0.000144089 [U]Use each side as a exponent to eulers constant e[/U] (1 + i) = e^0.000144089 1 + i = 1.000144099 i = 0.000144099 or [B].0144099%[/B]
WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512
WHAT SHOULD BE SUBTRACTED FROM -9876 TO OBTAIN -9512 We set up an arbitrary number x. Subtracted from is written as -9876 - x The phrase [I]to obtain[/I] means an equation, so we set -9876 - x equal to -9512 -9876 - x = -9512 To solve for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=-9876-x%3D-9512&pl=Solve']type this equation into our search engine[/URL] and we get: x = [B]364[/B]
When 20 is subtracted from 3 times a certain number, the result is 43
A certain number means an arbitrary variable, let's call it x x 3 times x 3x 20 is subtracted from 3 time x 3x - 20 The result is means equal to, so we set 3x - 20 equal to 43 for our algebraic expression [B]3x - 20 = 43 [/B] If you need to solve this, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-20%3D43&pl=Solve']equation calculator[/URL]: [B]x = 21[/B]
When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negati
When 28 is subtracted from the square of a number, the result is 3 times the number. Find the negative solution. Let the number be n. Square of a number: n^2 28 is subtracted from the square of a number: n^2 - 28 3 times the number: 3n [I]The result is[/I] mean an equation, so we set n^2 - 28 = 3n n^2 - 28 = 3n Subtract 3n from each side: n^2 - 3n - 28 = 3n - 3n The right side cancels to 0, so we have: n^2 - 3n - 28 = 0 This is a quadratic equation in standard form, so we [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-28%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']use our quadratic calculator[/URL] to solve: We get two solutions for n: n = (-4, 7) The question asks for the negative solution, so our answer is: [B]n = -4[/B]
When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unkn
When 39 is added to a number, the result is 40 times the number. Find the number. Let n be the unknown number. Write the translated equation below. [LIST=1] [*]39 added to a number is written as n + 39 [*]40 times the number is written as 40n [*]The result is means we have an equation, so set (1) equal to (2) [/LIST] n+ 39 = 40n Running [URL='http://www.mathcelebrity.com/1unk.php?num=n%2B39%3D40n&pl=Solve']n + 39 = 40n through the search engine[/URL], we get[B] n = 1[/B].
When 4 is subtracted from the square of a number, the result is 3 times the number. Find the positiv
When 4 is subtracted from the square of a number, the result is 3 times the number. Find the positive solution. Let the number be n. We have: n^2 - 4 = 3n Subtract 3n from each side: n^2 - 3n - 4 = 0 [URL='https://www.mathcelebrity.com/quadratic.php?num=n%5E2-3n-4%3D0&pl=Solve+Quadratic+Equation&hintnum=+0']Typing this quadratic equation into the search engine[/URL], we get: n = (-1, 4) The problem asks for the positive solution, so we get [B]n = 4[/B].
When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num
When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number. Find the number The phrase [I]a number, [/I]means an arbitrary variable, let's call it "x". 4 times a number, increased by 40, means we multiply 4 times x, and then add 40 4x + 40 100 decreased by the number means we subtract x from 100 100 - x The problem tells us both of these expressions are the same, so we set them equal to each other: 4x + 40 = 100 - x Add x to each side: 4x + x + 40 = 100 - x + x The x's cancel on the right side, so we have: 5x + 40 = 100 [URL='https://www.mathcelebrity.com/1unk.php?num=5x%2B40%3D100&pl=Solve']Typing this equation into the search engine[/URL], we get [B]x = 12[/B].
When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the num
When 4 times a number is increased by 40, the answer is the same as when 100 is decreased by the number The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x 4 times a number means we multiply x by 4: 4x Increased by 40 means we add 40 to 4x: 4x + 40 100 decreased by the number means we subtract x from 100: 100 - x The phrase [I]is the same as[/I] means equal to, so we set 4x + 40 equal to 100 - x 4x + 40 = 100 - x Solve for [I]x[/I] in the equation 4x + 40 = 100 - x [SIZE=5][B]Step 1: Group variables:[/B][/SIZE] We need to group our variables 4x and -x. To do that, we add x to both sides 4x + 40 + x = -x + 100 + x [SIZE=5][B]Step 2: Cancel -x on the right side:[/B][/SIZE] 5x + 40 = 100 [SIZE=5][B]Step 3: Group constants:[/B][/SIZE] We need to group our constants 40 and 100. To do that, we subtract 40 from both sides 5x + 40 - 40 = 100 - 40 [SIZE=5][B]Step 4: Cancel 40 on the left side:[/B][/SIZE] 5x = 60 [SIZE=5][B]Step 5: Divide each side of the equation by 5[/B][/SIZE] 5x/5 = 60/5 x = [B]12[/B] Check our work for x = 12: 4(12) + 40 ? 100 - 12 48 + 40 ? 100 - 12 88 = 88
When 54 is subtracted from the square of a number, the result is 3 times the number.
When 54 is subtracted from the square of a number, the result is 3 times the number. This is an algebraic expression. Let's take it in parts. The phrase [I]a number[/I] means an arbitrary variable, let's call it "x". x Square the number, means raise it to the 2nd power: x^2 Subtract 54: x^2 - 54 The phrase [I]the result[/I] means an equation, so we set x^2 - 54 equal to 3 [B]x^2 - 54 = 3[/B]
When 9 is subtracted from 5 times a number ,the result is 31
When 9 is subtracted from 5 times a number ,the result is 31 A number means an arbitrary variable, let's call it x. 5 times this number is written as 5x. 9 subtracted from this is written as 5x - 9 [I]The result[/I] means we have an equation, so we set [B]5x - 9 = 31[/B]. This is our algebraic expression. Now if we want to solve for x, we [URL='http://www.mathcelebrity.com/1unk.php?num=5x-9%3D31&pl=Solve']plug this equation into the search engine [/URL]and get [B]x = 8[/B].
When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at
When a dog noticed a fox, they were 60 meters apart. The dog immediately started to chase the fox at a speed of 750 meters per minute. The fox started to run away at a speed of 720 meters per minute. How soon will the dog catch the fox? The dog sits a position p. Distance = Rate x Time The dogs distance in minutes is D = 720t The fox sits at position p + 60 Distance = Rate x Time The fox's distance in minutes is D = 750t - 60 <-- Subtract 60 since the fox is already ahead 60 meters. We want to know when their distance (location) is the same. So we set both distance equations equal to each other: 720t = 750t - 60 [URL='https://www.mathcelebrity.com/1unk.php?num=720t%3D750t-60&pl=Solve']Using our equation calculator[/URL], we get [B]t = 2[/B]. Let's check our work: Dog's distance is 720(2) = 1440 Fox's distance is 750(2) - 60 = 1,440
When a number is doubled, the result is 36
When a number is doubled, the result is 36 Let the number be n. We have: 2n = 36 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2n%3D36&pl=Solve']equation solver[/URL], we see that [B]n = 18[/B]
When an alligator is born it is about 8 inches long each year they grow 12 inches determine the age
When an alligator is born it is about 8 inches long each year they grow 12 inches determine the age and years of 116 inch alligator? Calculate inches to grow to get to 116 116 - 8 = 108 Now figure out how many years it takes growing at 12 inches per year, using y as years 12y = 108 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=12y%3D108&pl=Solve']equation calculator[/URL], we get: [B]y = 9[/B]
When ringing up a customer, a cashier needs 3 seconds to scan each item and 9 seconds to process the
When ringing up a customer, a cashier needs 3 seconds to scan each item and 9 seconds to process the payment. Let m represent the number of items and s represent the number of seconds to ring up a customer. Build our equation R(m): [B]R(m) = ms + 9[/B]
When twice a number is reduced by 15 you get 95 what is the number
When twice a number is reduced by 15 you get 95 what is the number? The phrase [I]a number[/I] means an arbitrary variable, let's call it x. x [I]Twice[/I] x means we multiply x by 2 2x [I]Reduced by[/I] 15 means we subtract 15 2x - 15 [I]You get[/I] means equal to, as in an equation. Set 2x - 15 = 95 2x - 15 = 95 <-- This is our algebraic expression. [URL='https://www.mathcelebrity.com/1unk.php?num=2x-15%3D95&pl=Solve']Type 2x - 15 = 95 into the search engine[/URL] and we get [B]x = 55[/B].
Which of the following equations represents a line that is parallel to the line with equation y = -3
Which of the following equations represents a line that is parallel to the line with equation y = -3x + 4? A) 6x + 2y = 15 B) 3x - y = 7 C) 2x - 3y = 6 D) x + 3y = 1 Parallel lines have the same slope, so we're looking for a line with a slope of 3, in the form y = mx + b. For this case, we want a line with a slope of -3, like our given line. If we rearrange A) by subtracting 6x from each side, we get: 2y = -6x + 15 Divide each side by 2, we get: y = -3x + 15/2 This line is in the form y = mx + b, where m = -3. So our answer is [B]A[/B].
Which phrase is represented by the equation p equals kv
Which phrase is represented by the equation p equals kv [B]p varies directly as v[/B]
Whitney has already baked 2 cakes, and she can bake 1 cake with each additional stick of butter she
Whitney has already baked 2 cakes, and she can bake 1 cake with each additional stick of butter she buys. Write an equation that shows the relationship between the number of additional sticks of butter s and the number of cakes c. [LIST] [*]Let c, the number of cakes, be represented by f(s) where s are the number of sticks of butter. [*]We already have 2 cakes to start, and each additional stick of butter gets us one more cake. [/LIST] f(s) = 1s + 2 Simplify, since 1s is just s [B]f(s) = s + 2[/B]
Wilbie had candy to give to his 3 children. He first took 5 pieces and evenly divided the rest among
Wilbie had candy to give to his 3 children. He first took 5 pieces and evenly divided the rest among each child. Each child received 3 pieces. With how many pieces did he start? Let the starting candy amount be c. We're given: (c - 5)/3 = 3 Cross multiply: c - 5 = 3*3 c - 5 = 9 [URL='https://www.mathcelebrity.com/1unk.php?num=c-5%3D9&pl=Solve']Type this equation into the search engine[/URL], and we get: c = 14
Write a model that utilizes all three explanatory variables with no interaction or quadratic terms.
Write a model that utilizes all three explanatory variables with no interaction or quadratic terms. Choose the correct answer below. A. y i = B0 + B1x1 + B2x2 + B3x3 + e i B. y i = B0 + B1x1 + B2x2 + B3x3x2 + e i C. y i = B1x1 + B2x2 + B3x3 + ei D. None of the above equations satisfy all of the conditions [B]A. y i = B0 + B1x1 + B2x2 + B3x3 + e i[/B]
Write a system of equations to describe the situation below, solve using any method, and fill in the
Write a system of equations to describe the situation below, solve using any method, and fill in the blanks. Hugo is going to send some flowers to his wife. Somerville Florist charges $2 per rose, plus $39 for the vase. Dwaynes Flowers, in contrast, charges $3 per rose and $10 for the vase. If Hugo orders the bouquet with a certain number of roses, the cost will be the same with either flower shop. What would the total cost be? How many roses would there be? Let r be the number of roses and C(r) be the cost function. The vase is a one-time cost. Somerville Florist: C(r) = 2r + 39 Dwaynes Flowers C(r) = 3r + 10 Set them equal to each other: 2r + 39 = 3r + 10 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=2r%2B39%3D3r%2B10&pl=Solve']equation calculator[/URL], we get: [B]r = 29[/B]
Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7
Write an equation in slope-intercept form for the line with slope 4 and y-intercept -7 The standard equation for slope (m) and y-intercept (b) is given as: y = mx + b We're given m = 4 and y-intercept = -7, so we have: [B]y = 4x - 7[/B]
writing and solving equations
My daughter is having issues with a math problem for her homework. she tells me that I am doing it wrong but I am getting the correct answer... Can you please look at it and see if i am correct? The problem is: A painter charges $15.35 per hour, plus an additional amount for supplies. If he made $141.73 on a job where he worked 4 hours, how much did the supplies cost? I have the equation as: $15.35 * 4 = $141.73 - x ... I got the answer of $80.33 for supplies She is telling me that the teacher is wanting her to do the PEMDAS backwards but that is not working out for her and I am not understanding that at all. Any suggestions would help out Thanks, Tina
writing and solving equations
Your answer is correct. Here is how I set up the profit equation where h is the hours worked and x is the supply cost: P(h) = 15.35h + x We know P(4) = 141.73 P(4) = 15.35(4) + x 141.73 = 15.35(4) + x Simplify 141.73 = 61.4 + x Subtract 61.4 from each side: [B]x = 80.33[/B]
x - 5y = 6 for x
x - 5y = 6 for x Add 5y to each side to solve this literal equation for x. x - 5y + 5y = 6 + 5y Cancel the 5y on each side, we get: x = [B]6 + 5y[/B]
X plus 9 is equal to 3 times x minus 4
X plus 9 is equal to 3 times x minus 4 x plus 9: x + 9 3 times x minus 4: 3x - 4 The phrase [I]is equal to[/I] means an equation, so we set x + 9 equal to 3x - 4: [B]x + 9 = 3x - 4[/B]
x tripled less two is 5
x tripled less two is 5 x tripled means we multiply x by 3 3x Less two means we subtract 2 from 3x 3x - 2 [I]Is[/I] means equal to, so we set 3x - 2 equal to 5 [B]3x - 2 = 5[/B] [B][/B] To solve this equation, use our [URL='http://www.mathcelebrity.com/1unk.php?num=3x-2%3D5&pl=Solve']equation solver[/URL].
X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4
X varies directly with the cube root of y when x=1 y=27. Calculate y when x=4 Varies directly means there is a constant k such that: x = ky^(1/3) When x = 1 and y = 27, we have: 27^1/3(k) = 1 3k = 1 To solve for k, we[URL='https://www.mathcelebrity.com/1unk.php?num=3k%3D1&pl=Solve'] type in our equation into our search engine[/URL] and we get: k = 1/3 Now, the problem asks for y when x = 4. We use our variation equation above with k = 1/3 and x = 4: 4 = y^(1/3)/3 Cross multiply: y^(1/3) = 4 * 3 y^(1/3) =12 Cube each side: y^(1/3)^3 = 12^3 y = [B]1728[/B]
x/y = z - 8 for x
x/y = z - 8 for x We start by seeing that x is isolated. To remove y from the left side, we multiply each side of the equation by y: xy/y = y(z - 8) Cancelling y on the left side, we get our answer of: x = [B]y(z - 8) [MEDIA=youtube]_HNyGlnnQdQ[/MEDIA][/B]
Xavier has $132 to buy a video game. Each game costs $12. Write an equation to find the number of ga
Xavier has $132 to buy a video game. Each game costs $12. Write an equation to find the number of games Xavier can purchase. Let g be the number of games, we have a cost function C(g) C(g) = 12g We want to find g such that C(g) = 132 12g = 132 Divide each side by 12 [B]g = 11[/B]
y minus 10 is equal to the product of y and 8
y minus 10 is equal to the product of y and 8. Take this algebraic expression in 3 parts: Part 1: y minus 10 Subtract 10 from the variable y y - 10 Part 2: The product of y and 8 We multiply 8 by the variable y 8y Part 3: The phrase [I]is equal to[/I] means an equation, so we set y - 10 equal to 8y [B]y - 10 = 8y[/B]
y/2+c=d for y
Multiply each side by 2 to isolate y. y +2c = 2d Subtract 2c from each side of the equation: y = 2d - 2c This can also be written y = 2(d - c)
You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $1
You and a friend want to start a business and design t-shirts. You decide to sell your shirts for $15 each and you paid $6.50 a piece plus a $50 set-up fee and $25 for shipping. How many shirts do you have to sell to break even? Round to the nearest whole number. [U]Step 1: Calculate Your Cost Function C(s) where s is the number of t-shirts[/U] C(s) = Cost per Shirt * (s) Shirts + Set-up Fee + Shipping C(s) = $6.50s + $50 + $25 C(s) = $6.50s + 75 [U]Step 2: Calculate Your Revenue Function R(s) where s is the number of t-shirts[/U] R(s) = Price Per Shirt * (s) Shirts R(s) = $15s [U]Step 3: Calculate Break-Even Point[/U] Break Even is where Cost = Revenue. Set C(s) = R(s) $6.50s + 75 = $15s [U]Step 4: Subtract 6.5s from each side[/U] 8.50s = 75 [U]Step 5: Solve for s[/U] [URL='https://www.mathcelebrity.com/1unk.php?num=8.50s%3D75&pl=Solve']Run this through our equation calculator[/URL] to get s = 8.824. We round up to the next integer to get [B]s = 9[/B]. [B][URL='https://www.facebook.com/MathCelebrity/videos/10156751976078291/']FB Live Session[/URL][/B]
You and your friend are playing a number-guessing game. You ask your friend to think of a positive n
You and your friend are playing a number-guessing game. You ask your friend to think of a positive number, square the number, multiply the result by 2, and then add three. If your friend's final answer is 53, what was the original number chosen? Let n be our original number. Square the number means we raise n to the power of 2: n^2 Multiply the result by 2: 2n^2 And then add three: 2n^2 + 3 If the friend's final answer is 53, this means we set 2n^2 + 3 equal to 53: 2n^2 + 3 = 53 To solve for n, we subtract 3 from each side, to isolate the n term: 2n^2 + 3 - 3 = 53 - 3 Cancel the 3's on the left side, and we get: 2n^2 = 50 Divide each side of the equation by 2: 2n^2/2 = 50/2 Cancel the 2's, we get: n^2 = 25 Take the square root of 25 n = +-sqrt(25) n = +-5 We are told the number is positive, so we discard the negative square root and get: n = [B]5[/B]
You and your friend are saving for a vacation. You start with the same amount and save for the same
You and your friend are saving for a vacation. You start with the same amount and save for the same number of weeks. You save 75 per week, and your friend saves 50 per week. When vacation time comes, you have 950, and your friend has 800. How much did you start with, and for how many weeks did you save? [U]Let w be the number of weeks. Set up two equations where s is the starting amount:[/U] (1) s + 75w =950 (2) s + 50w = 800 [U]Rearrange (1) into (3) to solve for s by subtracting 75w[/U] (3) s = 950 - 75w [U]Rearrange (2) into (4) to solve for s by subtracting 50w[/U] (4) s = 800 - 50w [U]Set (3) and (4) equal to each other so solve for w[/U] 950 - 75w = 800 - 50w [U]Add 75w to each side, and subtract 950 from each side:[/U] 25w = 150 [U]Divide each side by w[/U] [B]w = 6[/B] Now plug w = 6 into (3) s = 950 - 75(6) s = 950 - 450 [B]s = 500[/B]
You are baking muffins for your class. There are 17 total students in your class and you have baked
You are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student. 2 muffins per student = 17*2 = 34 muffins. We have an equation with a given 5 muffins, how much do we need (x) to get to 34 muffins (2 per student): x + 5 = 34 To solve for x, we type this equation into our search engine and we get: x = [B]29[/B]
You are baking muffins for your class. There are 17 total students in your class and you have baked
You are baking muffins for your class. There are 17 total students in your class and you have baked 5 muffins. Write and solve an equation to find the additional number x of muffins you need to bake in order to have 2 muffins for each student. Write your equation so that the units on each side of the equation are muffins per student. [U]Calculate total muffins:[/U] Total muffins = 2 muffins per student * 17 students Total muffins = 34 [U]Set up the equation using x for muffins:[/U] [B]x + 5 = 34 [/B] [U]To Solve this equation for x, we [URL='https://www.mathcelebrity.com/1unk.php?num=x%2B5%3D34&pl=Solve']type it in our search engine[/URL] and we get:[/U] x = [B]29 [/B]
You are buying boxes of cookies at a bakery. Each box of cookies costs $4. In the equation below, c
You are buying boxes of cookies at a bakery. Each box of cookies costs $4. In the equation below, c represents the number of boxes of cookies you buy, and d represents the amount the cookies will cost you (in dollars). The relationship between these two variables can be expressed by the following equation: d=4c. Identify the dependent and independent variables. [B]The variable d is dependent, and c is independent since the value of d is determined by c.[/B]
You are comparing the costs of producing shoes at two different manufacturers. Company 1 charges $5
You are comparing the costs of producing shoes at two different manufacturers. Company 1 charges $5 per pair of shoes plus a $650 flat fee. Company 2 charges $4 per pair of shoes plus a $700 flat fee. How many pairs of shoes are produced when the total costs for both companies are equal? Let s be the number of shoes. We have two equations: (1) C = 5s + 650 (2) C = 4s + 700 Set the costs equal to each other 5s + 650 = 4s + 700 Subtract 4s from each side s + 650 = 700 Subtract 650 from each side [B]s =50[/B]
You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $
You are heading to Cedar Point for the day. It costs $50 to get in to the park and each ride costs $2 for a ticket. Write an expression for the total cost of going to Cedar Point where r is the number of rides. Set up the cost equation C(r): C(r) = Cost per ride * r rides + Park Fee [B]C(r) = 2r + 50[/B]
You are offered two different sales jobs. The first company offers a straight commission of 6% of th
You are offered two different sales jobs. The first company offers a straight commission of 6% of the sales. The second company offers a salary of $330 per week plus 2% of the sales. How much would you have to sell in a week in order for the straight commission offer to be at least as good? Let s be the sales and C be the weekly commission for each sales job. We have the following equations: [LIST=1] [*]C = 0.06s [*]C = 330 + 0.02s [/LIST] Set them equal to each other: 0.06s = 330 + 0.02s Subtract 0.02s from each side: 0.04s = 330 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.04s%3D330&pl=Solve']equation solver[/URL], we get [B]s = 8,250[/B]
You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet.
You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet. Company A charges $2.99 per square foot plus a $200 installation charge. Company B charges $19.99 per square yard plus a $500 installation charge. What is the best deal? Did you notice the word snuck in on this problem? Company B is given in square [I][B]yards[/B][/I], not feet. Let's convert their price to square feet to match company A. [U]Company B conversion:[/U] Since we have 1 square yard = 3 feet * 3 feet = 9 square feet, we need to solve the following proportion: $19.99/square yard * 1 square yard/9 feet = $19.99 square yard / 9 feet = $2.22 / square foot. Now, let's set up the cost equations C(s) for each Company in square feet (s) [LIST] [*]Company A: C(s) = 200 + 2.99s [*]Company B: C(s) = 500 + 2.22s [/LIST] The problem asks for s = 30 feet * 50 feet = 1500 square feet. So we want to calculate C(1500) [U]Company A:[/U] C(1500) = 200 + 2.99(1500) C(1500) = 200 + 4485 C(1500) = 4685 [U]Company B:[/U] C(1500) = 500 + 2.22(1500) C(1500) = 500 + 3330 C(1500) = 3830 Since [B]Company B[/B] has the lower cost per square foot, they are the better buy.
You bought a box of pens for $5 and some notepads for $3 each. You spent a total of $26.
You bought a box of pens for $5 and some notepads for $3 each. You spent a total of $26. Let p be the number of pens and n be the number of notepads. Our equation is: 5[B]p + 3n = 26[/B]
You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase
You buy a container of cat litter for $12.25 and a bag of cat food for x dollars. The total purchase is $19.08, which includes 6% sales tax. Write and solve an equation to find the cost of the cat food. Our purchase includes at cat litter and cat food. Adding those together, we're given: 12.25 + x = 19.08 To solve for x, [URL='https://www.mathcelebrity.com/1unk.php?num=12.25%2Bx%3D19.08&pl=Solve']we type this equation into our search engine[/URL], and we get: x = 6.83 Since the cat food includes sales tax, we need to remove the sales tax of 6% to get the original purchase price. Original purchase price = After tax price / (1 + tax rate) Original purchase price = 6.83/1.06 Original purchase price = [B]$6.44[/B]
You can get 2 different moving companies to help you move. The first one charges $150 up front then
You can get 2 different moving companies to help you move. The first one charges $150 up front then $38 an hour. The second one charges $230 then $30 an hour, at what exact time will Both companies cost the same [U]Company 1: We set up the cost equation C(h) where h is the number of hours[/U] C(h) = Hourly Rate * h + up front charge C(h) = 38h + 150 [U]Company 2: We set up the cost equation C(h) where h is the number of hours[/U] C(h) = Hourly Rate * h + up front charge C(h) = 30h + 230 The question asks for h when both cost equations C(h) are equal. So we set both C(h) equations equal to other: 38h + 150 = 30h + 230 To solve for h, we [URL='https://www.mathcelebrity.com/1unk.php?num=38h%2B150%3D30h%2B230&pl=Solve']type this equation into our search engine [/URL]and we get: h = [B]10[/B]
You can pay a daily entrance fee of $3 or purchase a membership for the 12 week summer season for $8
You can pay a daily entrance fee of $3 or purchase a membership for the 12 week summer season for $82 and pay only $1 per day to swim. How many days would you have to swim to make the membership worthwhile? Set up cost equations: Daily entrance fee: 3d where d is the number of days of membership Membership fee 82 + 1d Set them equal to each other 82 + 1d = 3d Subtract d from each side: 2d = 82 Divide each side by 2 [B]d = 41[/B]
You collect stamps. You give steven 21 stamps. At the end youbhave 3. How many stamps did you start
You collect stamps. You give steven 21 stamps. At the end youbhave 3. How many stamps did you start with? You start with s stamps. s You give Steven 21. Giving means you subtract from your total: s - 21 You have 3 left s - 21 = 3 To solve this equation for s, we t[URL='https://www.mathcelebrity.com/1unk.php?num=s-21%3D3&pl=Solve']ype it in our math engine[/URL] and we get: s = [B]24[/B]
You earned $141 last week babysitting and cleaning. You earned $5 per hour babysitting and $7 per ho
You earned $141 last week babysitting and cleaning. You earned $5 per hour babysitting and $7 per hour cleaning. You worked 9 more hours babysitting than cleaning. How many hours did you work last week? Let b be the hours of babysitting and c be the hours of cleaning. We're given two equations: [LIST=1] [*]b = c + 9 [*]5b + 7c = 141 [/LIST] Substitute equation (1) into (2): 5(c + 9) + 7c = 141 Multiply through: 5c + 45 + 7c = 141 Combine like terms: 12c + 45 = 141 [URL='https://www.mathcelebrity.com/1unk.php?num=12c%2B45%3D141&pl=Solve']Typing this equation into our search engine[/URL], we get: c = 8 Now substitute this value of c back into Equation (1): b = 8 + 9 b = 17 The total hours worked (t) is: t = b + c t = 17 + 8 t = [B]25[/B]
You had $22 to spend on 8 notebooks after buying them you had $6
If you have $6 left over, then 8 notebooks cost $22 - $6 = $16. 8 notebooks = $16 Divide each side of the equation by 8 Each notebook is $2
You have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account a
You have $140 in a savings account and save $10 per week. Your friend has $95 in a savings account and saves $19 per week. How many weeks will it take for you and your friend to have the same balance? [U]Set up the savings account S(w) for you where w is the number of weeks[/U] S(w) = 140 + 10w [U]Set up the savings account S(w) for your friend where w is the number of weeks[/U] S(w) = 95 + 19w The problem asks for the number of weeks (w) when the balances are the same. So set both equations equal to each other: 140 + 10w = 95 + 19w To solve this equation for w, [URL='https://www.mathcelebrity.com/1unk.php?num=140%2B10w%3D95%2B19w&pl=Solve']we type it in the search engine[/URL] and get: w = [B]5[/B]
You have $20 to spend on a taxi fare. The ride costs $5 plus $2.50 per kilometer.
You have $20 to spend on a taxi fare. The ride costs $5 plus $2.50 per kilometer. Let k be the number of kilometers. Total Cost = Cost per kilometer * number of kilometers + Fixed Cost With k for kilometers, 2.5 as cost per kilometer, and 5 as fixed cost, and 20 on total cost, we have: 2.5k + 5 = 20 To solve this equation for k, we [URL='https://www.mathcelebrity.com/1unk.php?num=2.5k%2B5%3D20&pl=Solve']type it in our math engine [/URL]and we get k = [B]6[/B]
You have $250,000 in an IRA (Individual Retirement Account) at the time you retire. You have the op
You have $250,000 in an IRA (Individual Retirement Account) at the time you retire. You have the option of investing this money in two funds: Fund A pays 5.4% annually and Fund B pays 7.9% annually. How should you divide your money between fund Fund A and Fund B to produce an annual interest income of $14,750? You should invest $______in Fund A and $___________in Fund B. Equation is x(.079) + (250,000 - x).054 = 14,750 .025x + 13,500 = 14,750 .025x = 1,250 [B]x = 50,000 for Fund A[/B] So at 5.4%, we have 250,000 - 50,000 = [B]200,000[/B] for the other fund B.
You have $37 to plant garden. If you spend $12.25 on seeds, how many packs of vegetable plants can
You have $37 to plant garden. If you spend $12.25 on seeds, how many packs of vegetable plants can you buy for 2.75 each? [U]How much do we have to spend on plants?[/U] $37 - 12.25 = $24.75 [U]Calculate how many vegetable plants we can buy. Set up an equation where x = vegetable plants[/U] 2.75x = 24.75 Divide each side by 2.75 [B]x = 9[/B]
You have $6.50 to make copies. It cost $0.45. Write and solve an equality that represents the number
You have $6.50 to make copies. It cost $0.45. Write and solve an equality that represents the number of copies Hoow many exact copies can you make? Let the number of copies be c. We have: 0.45c = 6.50 [URL='https://www.mathcelebrity.com/1unk.php?num=0.45c%3D6.50&pl=Solve']Type this equation into our search engine[/URL] and we get: c = 14.444 We round down and say we can make 14 copies. [B]c = 14[/B] Now, if the problem asks you for an [I]inequality[/I], we want to see how many copies we can make without exceeding our $6.50 spend. So it's less than or equal to: [B]c <= 14[/B]
You have a total of 42 math and science problems for homework. You have 10 more math problems than s
You have a total of 42 math and science problems for homework. You have 10 more math problems than science problems. How many problems do you have in each subject? Let m be the math problems and s be the science problems. We have two equations: (1) m + s = 42 (2) m = s + 10 Substitute (2) into (1) (s + 10) + s = 42 Combine like terms 2s + 10 = 42 Subtract 10 from each side 2s = 32 Divide each side by 2 [B]s = 16[/B] So that means m = 16 + 10 --> [B]m = 26 (m, s) = (26, 16)[/B]
You need to hire a catering company to serve meals to guests at a wedding reception. Company A charg
You need to hire a catering company to serve meals to guests at a wedding reception. Company A charges $500 plus $20 per guest. Company B charges $800 plus $16 per guest. For how many guests are the total costs the same at both companies? Set up the Cost equations for both companies where g is the number of guests: [LIST] [*]C(a) = 20g + 500 [*]C(b) = 16g + 800 [/LIST] Set each equation equal to each other and use our [URL='http://www.mathcelebrity.com/1unk.php?num=20g%2B500%3D16g%2B800&pl=Solve']equation solver[/URL] to get: [B]g = 75[/B]
You open up a savings account. Your initial deposit is $300. You plan to add in $50 per month to sav
You open up a savings account. Your initial deposit is $300. You plan to add in $50 per month to save up for college. Write an equation to represent the situation. Let m be the number of months. We have a Savings account function S(m): S(m) = Monthly deposit * number of months + Initial Deposit [B]S(m) = 50m + 300[/B]
You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a
You pay 510.00 to rent a storage unit for 3 months the total cost includes an initial deposit plus a monthly fee of 160.00. Write and equation that represents your total cost Y in dollars after X months. Set up the cost function Y where x is the number of months you rent [B]Y = 160x + 510[/B]
You purchase a car for $23,000. The car depreciates at a rate of 15% per year. Determine the value
You purchase a car for $23,000. The car depreciates at a rate of 15% per year. Determine the value of the car after 7 years. Round your answer to the nearest cent. Set up the Depreciation equation: D(t) = 23,000/(1.15)^t We want D(7) D(7) = 23,000/(1.15)^7 D(7) = 23,000/2.66002 D(7) = [B]8,646.55[/B]
You rent skates for $5 and pay $1 an hour for skating per person. Write an equation.
You rent skates for $5 and pay $1 an hour for skating per person. Write an equation. Let the number of hours be h. Our cost function C(h) is: C(h) = Cost per hour * hourly rate + rental fee Plugging in our numbers, we get: [B]C(h) = h + 5[/B]
You spend $91 shopping for new clothes. You spend $24 for a pair of jeans and 35$ for a pair of shoe
You spend $91 shopping for new clothes. You spend $24 for a pair of jeans and 35$ for a pair of shoes. You also buy 4 shirts that cost d dollars. How much is each shirt? Subtract the cost of the jeans and shoes to get the cost of the shirts: Cost of shirts = Shopping Spend - Cost of Jeans - Cost of Shoes Cost of shirts = $91 - $24 - $35 Cost of shirts = $32 We're given the cost of each shirt is s, and we bought 4 shirts. Therefore, we have: 4s = 32 [URL='https://www.mathcelebrity.com/1unk.php?num=4s%3D32&pl=Solve']Type this equation into the search engine[/URL], and we get the cost of each shirt s = [B]$8[/B]
You split $1,500 between two savings accounts. Account A pays 5% annual interest and Account B pays
You split $1,500 between two savings accounts. Account A pays 5% annual interest and Account B pays 4% annual interest. After one year, you have earned a total of $69.50 in interest. How much money did you invest in each account. Explain. Let a be the amount you invest in Account A. So this means you invested 1500 - A in account B. We have the following equation: 05a + (1500 - a).04 = 69.50 Simplifying, we get: 0.05a + 1560 - 0.04a = 69.50 0.01a + 60 = 69.50 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=0.01a%2B60%3D69.50&pl=Solve']equation solver[/URL], we get: [B]a = 950[/B] So this means Account B is b = 1500 - 950 = [B]550[/B]
you start with 150$ in year bank account if you save $28 a year with equation would model your savin
you start with 150$ in year bank account if you save $28 a year with equation would model your savings find equation. We create a savings function S(y) where y is the number of years since the start. S(y) = Savings per year * y + initial savings [B]S(y) = 28y + 150[/B]
You want to put 520 quarters in coin wrappers. You need one wrapper for every $10 in quarters. Write
You want to put 520 quarters in coin wrappers. You need one wrapper for every $10 in quarters. Write an equation you can use to find how many wrappers w you need First, calculate the number of quarters in $10: Quarters in $10 = Value of Quarters / Cost per quarter Quarters in $10 = 10/0.25 Quarters in $10 = 40 Now find out how many wrappers we need with each wrapper holding 40 quarters: Number of wrappers = Total quarters / Quarters per wrapper Number of wrappers =520/40 Number of wrappers = [B]13[/B]
You went to the State Fair and spent $20. If cotton candy costs $2 and a soda pop costs $1. Which eq
You went to the State Fair and spent $20. If cotton candy costs $2 and a soda pop costs $1. Which equation represents the relation between the number of cotton candy (c) and soda pops (s) you can buy? Our total cost for 20 at the state fair is: Cost of Cotton Candy + Cost of Soda = 20 We know that price = cost * quantity, so we have: 2c + 1s = 20 Since 1s is written as s, we have: [B]2c + s = 20[/B]
Youngs Modulus-Stress-Strain
Calculates any of the 3 items in the Youngs Modulus equation with stress and strain.
Your clothes washer stopped working during the spin cycle and you need to get a person in to fix the
Your clothes washer stopped working during the spin cycle and you need to get a person in to fix the washer. Company A costs $20 for the visit and $15 for every hour the person is there to fix the problem. Company B costs $40 for the visit and $5 for every hour the person is there to fix the problem. When would Company B be cheaper than Company A? Set up the cost functions: [LIST] [*]Company A: C(h) = 15h + 20 [*]Company B: C(h) = 5h + 40 [/LIST] Set them equal to each other: 15h + 20 = 5h + 40 Using our [URL='http://www.mathcelebrity.com/1unk.php?num=15h%2B20%3D5h%2B40&pl=Solve']equation solver[/URL], we get h = 2. With [B]h = 3[/B] and beyond, Company B becomes cheaper than Company A.
Your friends in class want you to make a run to the vending machine for the whole group. Everyone pi
Your friends in class want you to make a run to the vending machine for the whole group. Everyone pitched in to make a total of $12.50 to buy snacks. The fruit drinks are $1.50 and the chips are $1.00. Your friends want you to buy a total of 10 items. How many drinks and how many chips were you able to purchase? Let c be the number of chips. Let f be the number of fruit drinks. We're given two equations: [LIST=1] [*]c + f = 10 [*]c + 1.5f = 12.50 [/LIST] Rearrange equation 1 by subtracting f from both sides: [LIST=1] [*]c = 10 - f [*]c + 1.5f = 12.50 [/LIST] Substitute equation (1) into equation (2): 10 - f + 1.5f = 12.50 To solve for f, we [URL='https://www.mathcelebrity.com/1unk.php?num=10-f%2B1.5f%3D12.50&pl=Solve']type this equation into our search engine[/URL] and we get: [B]f = 5[/B] Now, substitute this f = 5 value back into modified equation (1) above: c = 10 - 5 [B]c = 5[/B]
Your mother gave you $13.32 With which to buy a present. This covered 3/5 of the cost. How much did
Your mother gave you $13.32 With which to buy a present. This covered 3/5 of the cost. How much did the present cost Let the present cost p. We set up the equation we're given: 3/5p = 13.32 [URL='https://www.mathcelebrity.com/1unk.php?num=3%2F5p%3D13.32&pl=Solve']Type this equation into our search engine[/URL] and we get: p = [B]$22.20[/B]
your starting salary at a new company is 45000. Each year you receive a 2% raise. How long will it t
your starting salary at a new company is 45000. Each year you receive a 2% raise. How long will it take you to make $80000? Let y be the number of years of compounding the 2% raise. Since 2% as a decimal is 0.02, we have the following equation for compounding the salary: 45000 * (1.02)^y = 80000 Divide each side by 45000: (1.02)^y = 1.77777777778 To solve this equation for y, we [URL='https://www.mathcelebrity.com/natlog.php?num=1.02%5Ey%3D1.77777777778&pl=Calculate']type it in our search engine[/URL] and we get: y = [B]29.05[/B] [B]Or just over 29 years[/B]
z/w=x+z/x+y for z
z/w=x+z/x+y for z This is a literal equation. Let's isolate z on one side. Subtract z/x from each side. z/w - z/x = x + y Factor our z on the left side: z(1/w - 1/x) = x + y Divide each side by (1/w - 1/x) z = x + y/(1/w - 1/x) To remove reciprocals in the denominator, we rewrite 1/w - 1/x with a common denominator xw (x - w)/xw Then multiply x + y by the reciprocal z = [B](x + y)xw/(x - w)[/B]
z=m-x+y, for x
z=m-x+y, for x This is a literal equation. Let's add subtract (m + y) from each side: z - (m + y) = m - x + y - (m + y) The m + y terms cancel on the right side, so we have: z - m - y = -x Multiply each side by -1 to isolate x: -1(z - m - y) = -(-x) x = [B]m + y - z[/B]
Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same a
Zalika thinks of a number. She subtracts 6 then multiplies the result by 5. The answer is the same as subtracting 5 from the number then multiplying by 4. The phrase [I]a number[/I] means an arbitrary variable, let's call it x. We're given two expressions in relation to this number (x): [U]She subtracts 6 then multiplies the result by 5[/U] [LIST] [*]Subtract 6: x - 6 [*]Multiply the result by 5: 5(x - 6) [/LIST] [U]She subtracts 5 from the number then multiplying by 4[/U] [LIST] [*]Subtract 6: x - 5 [*]Multiply the result by 5: 4(x - 5) [/LIST] Finally, the expression [I]is the same as[/I] means an equation, so we set the first expression equal to the second expression to make the following equation: 5(x - 6) = 4(x - 5) Now, let's solve the equation for x. To do this, we [URL='https://www.mathcelebrity.com/1unk.php?num=5%28x-6%29%3D4%28x-5%29&pl=Solve']type this equation into our search engine [/URL]and we get: x = [B]10[/B]
Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it tak
Zombies are doubling every 2 days. If two people are turned into zombies today, how long will it take for the population of about 600,000 to turn into zombies? Let d = every 2 days. We set up the exponential equation 2 * 2^d = 600,000 Divide each side by 2: 2^d = 300000 To solve this equation for d, we [URL='https://www.mathcelebrity.com/natlog.php?num=2%5Ed%3D300000&pl=Calculate']type it in our math engine[/URL] and we get d = 18.19 (2 day periods) 18.19 * days per period = 36.38 total days Most problems like this ask you to round to full days, so we round up to [B]37 days[/B].
zy-dm=ky/t for y
zy-dm=ky/t for y Isolate terms with y to solve this literal equation. Subtract zy from each side: zy - dm - zy = ky/t - zy Cancel the zy terms on the left side, we get: -dm = ky/t - zy Factor out y: y(k/t - z) = -dm Divide each side by (k/t - z) y = -dm/(k/t - z) (k/t - z) can be rewritten as (k - tz)/t We multiply -dm by the reciprocal of this quotient to get our simplified literal equation: y = [B]-dmt/(k - tz)[/B]
|(x-7)/5|<=4
|(x-7)/5|<=4 Set up two equations: [LIST=1] [*](x-7)/5 <= 4 [*](x-7)/5 > -4 [/LIST] Cross Multiply (1): x - 7 <= 20 Add 7 to each side: x <= 27 Cross Multiply (2): x - 7 > -20 Add 7 to each side: x > -13
�The shortest person in a class is 55 inches tall and tallest person in that class is 75 inches tall
The shortest person in a class is 55 inches tall and tallest person in that class is 75 inches tall. write an absolute value equation that requires the minimum and maximum height. Use X to represent heights. We write our inequality as: [B]55 <= X <= 75[/B]
"How to Find the Slope of a Line That Contains Points (-2.75, -0.75) and (-0.25, -8.25)"
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