Problem 7.7. In the classroom, there are several single desks (no more than one person can sit at each desk; there are no other desks in the classroom). During the break, a quarter of the students went out into the corridor, and the number of people left in the classroom was equal to 4/7 of the total number of desks. How many desks are in the room if there are no more than 30?


Answer: 21.

Solution. Note that the number of remaining students is $\frac{3}{4}$ of the initial number, so it must be divisible by 3. Let's denote it by $3x$. Let $y$ be the number of desks. Then

$$
3 x=\frac{4}{7} y
$$

from which $21 x=4 y$. Since 4 and 21 are coprime, $y$ must be divisible by 21. From the problem's condition, we know that $y \leqslant 30$, so $y=21$.