1. According to a sociological survey conducted in 7 "Y" grade, it was found that $20 \%$ of students interested in mathematics are also interested in physics, and $25 \%$ of students interested in physics are also interested in mathematics. Only Pete and Vasya are not interested in either of these subjects. How many people are there in 7 "Y", if it is known that there are more than 20 but less than 30?
# Solution

The number of people in 7 "I" excluding Petya and Vasya exceeds 18 but is less than 28. Let $n$ be the number of students interested in both mathematics and physics. Then, the total number of students interested in mathematics is $5n$, and the total number of students interested in physics is $4n$. Therefore, the number of students interested in mathematics or physics is $5n + 4n - n = 8n$ students (see figure).

![](https://cdn.mathpix.com/cropped/2024_05_06_4df8f76a1e5c1d2910b3g-1.jpg?height=160&width=254&top_left_y=1393&top_left_x=975)

Within the specified range, there is only one number that is a multiple of eight. Therefore, $8n = 24$, and the total number of students in the class is 26.

Answer: 26 people