## 35. Parent Meeting

At the end of the school year, the third-grade teachers met with some of their students' parents; exactly 31 people were present at this meeting. The Latin teacher was asked questions by 16 parents, the French teacher by 17, the English teacher by 18, and so on up to the math teacher, who was asked questions by all the parents present at the meeting. How many parents were present at the meeting?
35. Let $n$ be the number of parents present at the meeting, and $m$ be the number of teachers. The first teacher talked to $15+1$ parents, the second to $15+2$, and so on, ..., the $m$-th teacher talked to $15+m$ parents. But the last teacher was the math teacher, with whom all the parents talked. Therefore,

$$
15+m=n
$$

Since there were a total of 31 people at the meeting, then

$$
n+m=31
$$

Subtracting the first equation from the second, we get

$$
n-15=31-n
$$

i.e., $n=23$.

At the mentioned meeting, there were 23 parents of students (and 8 teachers).