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 $n$ . Now you make $n$ + one tenth of $n = 1.10n$ . And you'll lose $x \text{ percent}$ of that, after which you'll be back to $n$ .

So $1.1n - (x/100)(1.1n) = n$

$\rightarrow 1.1 - (1.1x/100) = 1$

$\rightarrow 0.1 = (1.1x/100)$

$\rightarrow 10 = 1.1x$

$\rightarrow x = 10/1.1$

$\rightarrow x = 9.0909... = 9\frac{1}{11}$ percent. So!