SOLUTION: Assume that y varies inversely as x.If y=8 when x =2.5,find x when y=2.

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Question 23460: Assume that y varies inversely as x.If y=8 when x =2.5,find x when y=2.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You write this proportion like this:
y+=+k%2Fx Where k is the constant of proportionality.
First, you need to find the value of k and you can do this because you are told that y = 8 when x = 2.5, so you substitute these values of y (8) and x (2.5) into the above equation and solve for k.
8+=+k%2F2.5 Multiply both sides by 2.5
%282.5%29%288%29+=+k
k+=+20
You can rewrite the first equation with the value of k included.
y+=+20%2Fx
Now solve the problem of finding the value of x when y = 2 by substituting 2 for y in the last equation.
2+=+20%2Fx Multiply both sides by x
2x+=+20 Finally, divide both sides by 2.
x+=+10 This is the answer.