Question 5967
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 {{{ R = P - 0.20P }}} 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 {{{ R + cR = P }}} 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:


{{{ P-0.20P + c(P-0.20P) = P }}}


{{{ -0.20P + c(P-0.20P) = 0 }}} <--- Subtract P from both sides.


{{{ c(P-0.20P) = 0.20P }}} <--- Add 0.20P to both sides


{{{ c = 0.20P/(P-0.20P) }}} <---- Divide both sides by (P-0.20P) to solve for c


{{{ c = 0.20P/P(1-0.20) }}} <---- Factor out the P in the denominator


{{{ c = 0.20/0.80 }}} <----- The P's cancel. This says that it doesn't matter how many units you'll start with.


{{{ c = 0.25 }}} <----- 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.