7.12. In the class, a test was conducted. It turned out that the average grade for boys is 4; for girls, it is 3.25; and for everyone together, it is 3.6. How many boys and how many girls took the test, if it is known that the class has more than 30 and fewer than 50 students
7.12. Let there be $x$ boys and $y$ girls in the class. Then $\frac{4 x + 3.25 y}{x + y} = 3.6$, i.e., $8 x = 7 y$. Therefore, $x = 7 a$ and $y = 8 a$ for some integer $a$. Hence, the number $x + y = 15 a$ is divisible by 15. The only number divisible by 15 that is greater than 30 and less than 50 is 45. Thus, $x = 21$ and $y = 24$.