Problem 1. In one class, there are 24 students. In this class, the number of boys is equal to $\frac{3}{5}$ of the number of girls. How many boys and how many girls are there in the class?
Solution. First method. Since the number of boys is $\frac{3}{5}$ of the number of girls, we conclude that for every 3 boys, there are 5 girls. Therefore, the students in this class can be divided into groups of $3+5=8$ children. This means we have $24: 8=3$ such groups. In each group, there are 3 boys and 5 girls, which means there are $3 \cdot 3=9$ boys and $3 \cdot 5=15$ girls in the class.

Second method. If we denote the number of girls in the class by $x$, then the number of boys is $\frac{3}{5} x$. Therefore, the total number of students in the class is $x+\frac{3}{5} x$, and since this number is equal to 24, we get the equation $x+\frac{3}{5} x=24$. Further, we have $\frac{8}{5} x=24$, so $8 x=24 \cdot 5$, or $x=(24 \cdot 5): 8=15$. Thus, there are 15 girls and $24-15=9$ boys in the class.