SOLUTION: If y is inversely proportional to the cube of x, what percent does y change if x decreases by by 25%?

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Question 1199169: If y is inversely proportional to the cube of x, what percent does y change if x decreases by by 25%?
Found 3 solutions by math_helper, MathTherapy, greenestamps:
Answer by math_helper(2461) About Me  (Show Source):
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+y+=+k%2A%281%2Fx%5E3%29+

+x%5B2%5D+=+%283%2F4%29x+  <<< x%5B2%5D is 75% (=100%-25%) of x

+y%5B2%5D+=+k%281%2F%28x%5B2%5D%29%5E3%29+ 





Substitute y for k%281%2Fx%5E3%29+ 



+y%5B2%5D+=+%2864%2F27%29y+  or approx. +y%5B2%5D+=+2.37y+



Percentage change in y:  +%28y%5B2%5D-y%29%2Fy+%2A+100+=+%282.37y+-+y%29%2Fy+%2A+100+ = 137%

Answer by MathTherapy(10555) About Me  (Show Source):
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If y is inversely proportional to the cube of x, what percent does y change if x decreases by by 25%?
matrix%281%2C3%2C+y%2C+%22=%22%2C+k%2Fx%5E3%29 ----- y inversely proportional to cube of x
matrix%281%2C3%2C+y%5B2%5D%2C+%22=%22%2C+k%2F%28.75%5E3x%29%29 ----- Substituting .75 for x, since after a 25% reduction, 75% (.75) remains 

Comparing y and y2, we see a CHANGE from matrix%281%2C3%2C+1%2F1%2C+to%2C+1%2F.75%5E3%29
Therefore, change in y after 25% reduction in x =

Answer by greenestamps(13203) About Me  (Show Source):
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While the responses from the other two tutors are fine, there is no need to use a formal proportion or to find the constant of proportionality, as they did in their responses. There is a much faster informal path to the answer.

The value of x decreases by 25% or 1/4, which means the new value is 3/4 of the old value.

Since the value of y is inversely proportional to the cube of x, the value of y changes by a factor of (4/3)^3 = 2.37 to 2 decimal places.

An increase by a factor of 2.37 means a percent increase of

100(2.37-1) = 100(1.37) = 137

ANSWER: y increases by 137% when x decreases by 25%