## Task 1 - 310821

In a school class, every student is 13 or 14 years old; both age specifications actually occur in this class. If you add up all these (calculated as whole numbers) age specifications, the sum is 325.

Determine whether the number of students in this class is uniquely determined by these findings! If this is the case, state the number of students!
If $x$ and $y$ are the number of 13- and 14-year-old students, respectively, then

$$
13 x + 14 y = 325 = 13 \cdot 25
$$

Thus, $14 y$ is divisible by 13, and therefore $y$ is also divisible by 13. From the problem statement, we also know that $y > 0$ and $x > 0$. Due to (1), $14 y < 325$, and consequently $14 y < 14 \cdot 26$, $y < 26$.

Therefore, the only possibility is $y = 13$. From (1), we have $13 \cdot (x + 14) = 13 \cdot 25$; thus $x + 14 = 25$, $x = 11$.

Therefore, the number of students in the class is uniquely determined by the given conditions; it is $x + y = 24$.