Exercise 1. Fred and Sarah are the eldest of the same large family. Fred has twice as few brothers as sisters, while Sarah has as many sisters as brothers.

How many children are there in this family?
Solution to Exercise 1 Let $\mathrm{f}$ be the number of girls and $\mathrm{g}$ be the number of boys in this family.

Fred therefore has $g-1$ brothers and $f$ sisters, and the text states that $f=2(g-1)$. On the other hand, Sarah has $\mathrm{f}-1$ sisters and $\mathrm{g}$ brothers, and the statement tells us that $\mathrm{f}-1=\mathrm{g}$.

By substituting $g$ with $\mathrm{f}-1$ in the first equation, we get $\mathrm{f}=2 \cdot(\mathrm{f}-2)$, which leads to $\mathrm{f}=4$ and then $\mathrm{g}=\mathrm{f}-1=3$, resulting in a total of 7 children.