<<<  is 75% (=100%-25%) of x

 





Substitute y for  



  or approx. 



Percentage change in y:   = 137% 

Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
 If y is inversely proportional to the cube of x, what percent does y change if x decreases by by 25%?

 ----- y inversely proportional to cube of x
 ----- Substituting .75 for x, since after a 25% reduction, 75% (.75) remains 

Comparing y and y2, we see a CHANGE from 
Therefore, change in y after 25% reduction in x = 
 

Answer by greenestamps(13203)   (Show Source): You can put this solution on YOUR website!
 


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%


 

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