Problem 2. A group of students went to the park to relax. If 6 students sit on each bench, then there is no place for two of them, but if 7 students sit on each bench, then 3 seats remain empty. How many benches were there in the park and how many students were in the group?
Solution. Let $x$ be the number of benches in the park. If 6 students sit on each bench, then the number of students is $6 x+2$, since two have no place. If, on the other hand, 7 students sit on each bench, then the number of students will be $7 x-3$, since 3 places remain empty. Since the number of students is the same in both cases, it follows that $6 x+2=7 x-3$, from which we get $x=5$. Thus, there are 5 benches, and the number of students is $6 x+2=6 \cdot 5+2=32$.