According to a survey conducted in class 7 "E", it was found that $20 \%$ of the students interested in mathematics are also interested in physics, and $25 \%$ of the students interested in physics are also interested in mathematics. Only Pete and Vasya are not interested in either of these subjects. How many students are there in 7 "E", if it is known that the number is more than 20 but less than 30?
The number of people in 7 "E" 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 \( 5n + 4n - n = 8n \) (see the figure).

![](https://cdn.mathpix.com/cropped/2024_05_06_df0545ffb539121f37feg-34.jpg?height=172&width=263&top_left_y=2721&top_left_x=903)

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.