2. A team consisting of boys and girls from the Rostov region went to a CS:GO esports tournament. The average number of points scored by the girls turned out to be 22, by the boys - 47, and the average number of points for the entire team - 41. What is the percentage of girls in this team?
Solution. Let the number of girls be $x$, the number of boys be $y$, and the total points scored by them be $S_{1}$ and $S_{2}$ respectively. From the conditions, the following equations can be derived: $\frac{S_{1}}{x}=22, \frac{S_{2}}{y}=47$ and $\frac{S_{1}+S_{2}}{x+y}=41$. Then $S_{1}=22 x$ and $S_{2}=47 y$, from which $\frac{22 x+47 y}{x+y}=41$. Consider the left part of the last equation: $\frac{22 x+47 y}{x+y}=\frac{22 x+22 y+25 y}{x+y}=22+\frac{25 y}{x+y}$. Therefore, $22+\frac{25 y}{x+y}=41$ or $\frac{y}{x+y}=\frac{19}{25}$. Since $\frac{19}{25}=\frac{76}{100}$, the proportion of boys is $76\%$, and thus the proportion of girls is $24\%$. Answer: $\mathbf{24\%}$.