Problem 9.1. Fisherman Vasya caught several fish. The three largest fish, accounting for $35 \%$ of the total catch weight, he put in the refrigerator. The three smallest, accounting for $5 / 13$ of the weight of all the remaining fish, the fisherman gave to the cat. Vasya ate all the rest of the fish he caught. How many fish did Vasya catch?
Answer: 10.

Solution. From the condition, it follows that the cat got $65 \% \cdot \frac{5}{13}=25 \%$ of the weight of the catch. Therefore, Vasya ate $40 \%$ of the caught fish. If we denote by $x$ the number of fish eaten by Vasya, then the average weight of the eaten fish as a percentage of the total catch weight is 40/ $x$. According to the condition, the specified value does not exceed the average weight of the fish in the refrigerator and is not less than the average weight of the fish eaten by the cat. As a result, we get the inequality

$$
\frac{35}{3} \leqslant \frac{40}{x} \leqslant \frac{25}{3}
$$

which is satisfied only by $x=4$. Thus, the total number of caught fish is $4+3+3=10$.

## Criteria

Any correct solution to the problem is worth 7 points. In the absence of such a solution, the following criteria are summed:

## 2 6. The percentage of fish eaten by Vasya is correctly calculated.

2 6. At least one of the inequalities $\frac{35}{3} \leqslant \frac{40}{x} \leqslant \frac{25}{3}$ is formulated.

The following criterion is applied only in the absence of points for other advancements:

## 16. The correct answer is provided.