Combined Variation

If y varies directly as x and inversely as z, and y = 24 when x = 48 and z = 4, find x when y = 44 and z = 6.

• 126

• 132

• 148

• 154

If f varies directly as g and inversely as the square of h, and f = 20 when g = 50 and h = 5, find f when g = 18 and h = 6.

• 4

• 5

• 8

• 10

If y varies jointly as a and b and inversely as the square root of c, and y = 12 when a = 3, b = 2, and c = 64, find y when a = 5, b = 2, and c = 25.

• 8

• 16

• 24

• 32

The number of minutes needed to solve an exercise set of variation problems varies directly as the number of problems and inversely as the number of people working on the solutions. It takes 4 people 36 minutes to solve 18 problems. How many minutes will it take 6 people to solve 42 problems.

• 56 minutes

• 52 minutes

• 48 minutes

• 44 minutes

If x varies directly as y and inversely as z, and x = 10 when y = 5 and z = 3, for what value of z will x = 3 and y = 4?

• 2

• 4

• 6

• 8

The time it takes you to complete a puzzle is directly proportional to the number of pieces and inversely proportional to how many people are working on it. You and your three friends can complete a 1,000 piece puzzle in 2 hours. How long would it take you to complete a 2,500 piece puzzle?

• 8 hours

• 9 hours

• 10 hours

• 11 hours

z varies inversely with x and directly with y. If x = 4, y = 48 and z = -2, find x when z = 8 and y = 96.

• -2

• -1

• 0

• 1

z varies inversely with x and directly with y. If x = 1/2, y = 5 and z = 20, find x when z = -4 and y = 8.

• 1

• 2

• 3

• 4

The formula for Combined Variation is represented as:

• y = kx

• y = k/x

• y = kxz

• y = kx/z

If p varies directly as the square of q and inversely as the square root of r, and p = 60 when q = 6 and r = 81, find p when q = 8 and r = 144.

• 70

• 80

• 90

• 100