SOLUTION: Quantity z varies jointly as x and the cube of y. If z = 96 when x = 2 and y = 2, find z when x = 3 and y = 3.

Question 1172670: Quantity z varies jointly as x and the cube of y. If z = 96 when x = 2 and y = 2, find z when x = 3 and y = 3.

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52800) (Show Source): You can put this solution on YOUR website!
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Based on the problem's statement, you can write this proportion = . It is the same as = , or, equivalently, 6 = . It implies z = 6*81 = 486. ANSWER

Solved.

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@greenestamps, thank you for your notice.

I just corrected my post, and now the corrected version is here.

Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

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(for tutor @ikleyn)....

... varies jointly as x and the CUBE of y..

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Tutor @ikleyn has provided a response showing one way (of many!) to approach a problem like this.

Another common method is to determine the constant of variation from the given data...

... and then evaluate the formula with that constant and the new data.

And here is the way I myself find easiest to use....

z is 96 when x is 2 and y is 2.
When x changes from 2 to 3, the value of z changes by a factor of 3/2.
When y changes from 2 to 3, the value of z changes by a factor of (3/2)^3.

The "new" value of z is

Different students will find different methods more to their liking; try these different methods and find what "works" for you.

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