## Task 4 - 110734

Fritz tells:

"In our class, there are exactly twice as many girls as boys. If there were 5 fewer boys and 5 fewer girls, then we would have exactly three times as many girls as boys."

Determine the number of all girls and all boys in this class!
If the number of boys in this class is denoted by $x$, then the number of girls is $2x$. Therefore, the total number of students in the class is $3x$ because $x + 2x = 3x$.

If there were 5 fewer boys and 5 fewer girls, the total number of students would be $3x - 10$. According to the problem, we then have

$$
3x - 10 = (x - 5) + 3(x - 5)
$$

from which we get $x = 10$. Therefore, the class has exactly 30 students, with 20 girls and 10 boys.