## Task 2 - 230822

A class is divided into learning brigades in such a way that the number of members in each brigade is 2 more than the number of brigades. If one fewer brigade had been formed, each brigade could have had 2 more members.

Show that the number of students in this class can be uniquely determined from this information, and give this number!
If the number of brigades is denoted by $x$, then each brigade has $(x+2)$ students, and the class consists of $x(x+2)$ students.

If one fewer brigade had been formed, there would have been $(x-1)$ brigades with $(x+4)$ students each. This would result in a student count of $(x-1)(x+4)$. Therefore, we have

$$
x(x+2)=(x-1)(x+4) \quad \Rightarrow \quad x=4
$$

Thus, 4 brigades were formed, each with 6 students. Therefore, there are a total of 24 students in this class.