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.

Algebra ->  Test -> 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.       Log On


   

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) About Me  (Show Source):
You can put this solution on YOUR website!
.

Based on the problem's statement, you can write this proportion


    96%2F%282%2A2%5E3%29 = z%2F%283%2A3%5E3%29.


It is the same as


    96%2F16 = z%2F81,  or,  equivalently,  6 = z%2F81.


It implies  z = 6*81 = 486.    ANSWER

Solved.


. . . . . . . .

@greenestamps, thank you for your notice.

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



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


***************************************************
(for tutor @ikleyn)....

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

***************************************************

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...
z+=+kxy%5E3
96+=+k%282%29%282%5E3%29+=+16k
k+=+96%2F16+=+6

... and then evaluate the formula with that constant and the new data.
z+=+6xy%5E3
z+=+6%283%29%283%5E3%29+=+6%2881%29+=+486

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

%2896%29%283%2F2%29%283%2F2%29%5E3+=+96%2881%2F16%29+=+81%2A6+=+486

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