In a certain mathematical competition, $31.66\%$ of the participants were girls. $3.41\%$ of the girls qualified for the final. A total of 41 students received awards. The number of awarded girls was $4.8\%$ of the girls who qualified for the final, while the number of boys who placed was $1\%$ of all the participants (boys and girls combined) in the first round. How many students participated in the competition in total?
Let the number of all participants be $x$. According to the problem, the number of girls who received an award is:

$$
x \cdot \frac{31.66}{100} \cdot \frac{3.41}{100} \cdot \frac{4.8}{100}
$$

The number of boys who achieved a placement is $\frac{x}{100}$. Therefore,

$$
\begin{gathered}
\frac{31.66 \cdot 3.41 \cdot 4.8 x}{100^{3}}+\frac{x}{100}=41 \\
518.23088 x+100^{2} x=41000000
\end{gathered}
$$

from which

$$
x \approx \frac{41000000}{10518}=3989
$$

Eva Gergö (Maxim Gorkij School VII. grade)