## How to Solve Age Problems Part 3

This is the third part of the Solving Age Problems Series. In this part, we will solve age problems with a variety of formats and difficulty that are not discussed in the first two parts. We have already solved six problems in the first and second part, so we start with the seventh problem.

Example 7

Bill is four times as old as Carol. One fifth of Bill’s age added to one half Carol’s age is equal to $13$ years. How old are both of them?

Scratch work

Bill is older than Carol and he is four times older. This means that if Carol is $x$ years old, then Bill is $4x$ years old. Now, one fifth of Bill’s age is $\frac{1}{5}(4x)$ and one half of Carol’s age is $\frac{1}{2}x$. Add these together and you get $13$. Now, we have an equation. » Read more