2410.42 – Pompeii Geothermal Corp. Wages

You work for the Pompeii Geothermal Corporation, based in the southern part of Ohio. Last year you got a 10 percent pay raise. But now times are tough, and you and your colleagues have agreed to go back to your old pay rates. As a matter of interest, by what percent are your wages being lowered to get you back to where you were before you got your raise?

Solution

This problem is a good examplar of that saying, "Every problem has an answer that is simple, obvious, and wrong." That answer here is 10 percent.

But let's look closely. You used to make nn. Now you make nn + one tenth of n=1.10nn = 1.10n. And you'll lose xx percent of that, after which you'll be back to nn. So,

1.1n−(x100)(1.1n)=n1.1−1.1x100=10.1=1.1x10010=1.1xx=101.1x=9.0909...=9111%\begin{align*}1.1n - \left(\dfrac{x}{100}\right)(1.1n) &= n \\[1em]1.1 - \dfrac{1.1x}{100} &= 1 \\[1em]0.1 &= \dfrac{1.1x}{100} \\[1em]10 &= 1.1x \\[1em]x &= \dfrac{10}{1.1} \\[1em]x &= 9.0909... = 9\dfrac{1}{11} \%\end{align*}