Question 1202215: If y varies jointly as m and p and inversely as the cube root of w. If y = 12, when m = 3, p = 2, and w = 512, find y when m = 5, p = 2, and w = 125.
Found 4 solutions by mananth, josgarithmetic, greenestamps, ikleyn:
Answer by mananth(16946)   (Show Source):
You can put this solution on YOUR website! If y varies jointly as m and p and inversely as the cube root of w. If y = 12, when m = 3, p = 2, and w = 512, find y when m = 5, p = 2, and w = 125.
y varies jointly as m and p and inversely as the cube root of w
If y = 12, when m = 3, p = 2, and w = 512, Find k
12= k* (3*2)/512
k = 12*512/6
k = 1024
You know k now
find y when m = 5, p = 2, and w = 125. k=1024
plug in the equation and find y
Answer by josgarithmetic(39617)  (Show Source):
You can put this solution on YOUR website! -----------------------------------------------------------------------
y varies jointly as m and p and inversely as the cube root of w.
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Transcribes exactly as, 
Use the other given data to solve for value for k.
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Answer by greenestamps(13200)  (Show Source):
You can put this solution on YOUR website!
If you need to find the formula relating y, m, p, and w, then do what the other tutors showed: use the given data to determine the proportionality constant k to find the formula and then plug in the new data.
Note one tutor showed only the formula without evaluating the constant and without working the problem; the other tutor didn't read the problem correctly.
But if you only need to answer this one question, there is no need to do all that work. You can answer the question by analyzing how the changes in the parameters m, p, and w change the value of y.
The given value of y is 12.
y varies directly as m; the value of m changes from 3 to 5, a factor of 5/3; the change in m from 3 to 5 causes a change in y from 12 to 12*(5/3) = 20.
y varies directly as p; the value of p does not change, so the value of y does not change.
y varies inversely as the cube root of w. The cube root of w changes from 8 to 5, a factor of 5/8. Since the variation is inverse for w, the change in the value of w changes the value of y by a factor of 8/5; the final value of y is 20*(8/5) = 32.
ANSWER: 32
Without all the words....
(12)*(5/3)*(2/2)/(5/8) = 20/(5/8) = 20(8/5) = 32
Answer by ikleyn(52786)  (Show Source):
You can put this solution on YOUR website! .
To a Math composer, who created this problem.
Don't you think that the very first "If" is a superfluous word in this composition ?
It would be much better if you EXCLUDE it from this and from other similar problems that you will create in the future.
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