Problem 3. At an open-air concert, 950 visitors, men and women, were present. How many visitors were men, and how many were women, if for every 9 men there were 10 women.
Solution. Let's denote the number of groups of 9 men and 10 women by \(a\).

From the condition of the problem, it follows that

\[
\begin{aligned}
& 9 a+10 a=950 \\
& 19 a=950 \\
& a=50
\end{aligned}
\]

Thus, at the concert, there were \(9 a=9 \cdot 50=450\) men and \(10 a=10 \cdot 50=500\) women.