## 136. Math Puzzle $9 / 76$

In a residential area, the number of retirees makes up $40 \%$ of the eligible voting population and $25 \%$ of the total population.

How are the population groups of retirees, other adults, and children and youth who are not yet eligible to vote distributed in the residential area in percentage terms?
In the residential area, let $r \%$ be the percentage of retirees, $e \%$ the percentage of other adults, and $k \%$ the percentage of children and teenagers. Then we have:

$$
r=0.4(r+e), \quad r=0.25(r+e+k), \quad r+e+k=100 \%
$$

Result: $r=25 \% ; e=37.5 \% ; k=37.5 \%$.