7.4 In the class, there are more than 30 people but less than 40. Any boy is friends with three girls, and any girl is friends with five boys. How many people are in the class?
Answer: 32

Solution. Let $\mathrm{m}$ be the number of boys, $\mathrm{d}$ be the number of girls, and $\mathrm{r}$ be the number of friendly pairs "boy-girl". According to the problem, $\mathrm{r}=3 \mathrm{~m}$ and $\mathrm{r}=5 \mathrm{~d}$. Therefore, r is divisible by 3 and 5, and thus by 15: $\mathrm{r}=15 \mathrm{k}$. Then $\mathrm{m}=5 \mathrm{k}, \mathrm{d}=3 \mathrm{k}$, and the total number of students is $\mathrm{m}+\mathrm{d}=8 \mathrm{k}$, which means it is divisible by 8. The only number between 30 and 40 that is divisible by 8 is 32.