jmc

Let the percentage of people in Mathopolis who are children be $x$. The percentage of adults is then $1-x$. Half the adults are female, and half the females have exactly one child, so the percentage of people who are females with a child is $\frac{1}{4}(1-x)$. This percentage is equal to the percentage of children, since there is a correspondence between a mother and a child. So we have the equation $x=\frac{1}{4}(1-x)$. Solving for $x$ yields $x=1/5$, or $\boxed{20}$ percent.