3. There are three boxes $A$, $B$, and $C$, which contain 100, 50, and 80 balls of the same size, respectively. Each box contains some black balls. It is known that box $A$ has 15 black balls. If a box is randomly selected from the three boxes and then a ball is randomly drawn from this box, the probability of drawing a black ball is $\frac{101}{600}$. Then, the maximum number of black balls in box $C$ is $\qquad$.
3. 22 .

Assume the number of black balls in boxes $B$ and $C$ are $y$ and $x$ respectively. Then the probability of randomly drawing a black ball is
$$
\begin{array}{l}
\frac{1}{3} \times \frac{15}{100}+\frac{1}{3} \times \frac{y}{50}+\frac{1}{3} \times \frac{x}{80}=\frac{101}{600} \\
\Rightarrow 60+8 y+5 x=202 \\
\Rightarrow x=\frac{142-8 y}{5}=28-y+\frac{2-3 y}{5}
\end{array}
$$
$\Rightarrow y$'s unit digit is 4 or 9.
Therefore, the smallest $y=4$, corresponding to $x=22$.