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Question 5967: Sales reduction force a factory to cut back its output by 20%. By what percent must the reduced sales be increased to allow production to be brought back to normal?
Answer by prince_abubu(198)   (Show Source):
You can put this solution on YOUR website! They didn't specify how many units you should start with, right? So let's just say that it could be any number P (that is big enough to be real life enough).
They say that they'll have to cut back production by 20%. That's 20% of what they have now. So far then, we've got  where R is the reduced amount of production by 20%.
OK. So then they ask what percent should R be increased by to get back to that original P, right? No, it's not 20%, since 20% of the reduced price is less than the 20% used to reduce P to R before. In other words, increasing the reduced by 20% won't get you back to where you were.
So  is the equation we'll use. We'll have to solve for c to get that percentage increase. First up, we'll have to do a substitution. Substitute P - 0.20P for R:
 <--- Subtract P from both sides.
 <--- Add 0.20P to both sides
 <---- Divide both sides by (P-0.20P) to solve for c
 <---- Factor out the P in the denominator
 <----- The P's cancel. This says that it doesn't matter how many units you'll start with.
 <----- Finally, c = 25%. AKA, if you reduce anything by 20% of its size, you'll have to increase the shrunken size by 25% to get back to the original size.
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