Problem 1. Petya was given several physics problems and several math problems for homework. All the problems solved by Petya constitute $5 \%$ of the total number of physics problems and $20 \%$ of the total number of math problems. What percentage of the total number of problems did Petya solve?
Solution. Answer: $4 \%$.

Let Pete solve $N$ problems. This constitutes $5 \%$ ( $\frac{1}{20}$ of) the physics problems, so the total number of physics problems was $20 \mathrm{~N}$. Similarly, the number of math problems was $5 N$, so the total number of problems assigned was $20 N + 5 N = 25 N$. The problems solved by Pete constitute $\frac{N}{25 N} \cdot 100 \% = 4 \%$.

## Criteria

The largest suitable criterion is used:

7 points. Any complete solution to the problem.

7 points. Any complete solution to the problem, but the answer is given not in percentages, but as a fraction $\frac{1}{25}$ or 0.04.

3 points. Only the correct answer is given.