## Task B-3.2.

Tennis player Duje had a $50 \%$ win rate at the beginning of the clay tournament. After the first played clay tournament, where he had three wins and one loss, his win rate was greater than $52 \%$. After the second played clay tournament, where he had four wins and one loss, his win rate was less than $56 \%$. How many matches did Duje play before the clay tournament if we know that by the end of the season he played twice as many matches as before the clay tournament and won $u$ $60 \%$ of the matches?
## Solution.

Let $2n$ be the number of matches Duje played before the clay court tournaments. The number of victories is equal to $n$ since $\frac{n}{2n}=0.5$.

After the first tournament, with 3 victories in 4 matches played, we have

$$
\begin{aligned}
\frac{n+3}{2n+4} & >0.52 \\
25n+75 & >26n+52 \\
n & < \frac{49}{3} .
\end{aligned}
$$

Thus, $n \geqslant 17$.

It follows that $n \in\{17,18,19,20,21,22\}$.

At the end of the season, we have

$$
\begin{aligned}
\frac{n+x}{4n} & =0.6 \\
2.4n & =n+x \\
1.4n & =x
\end{aligned}
$$

Since $x$ is a natural number, $n$ must be equal to 20, meaning Duje played 40 matches.