Question 3
Three boxes $A$, $B$ and $C$, contain $100$, $50$ and $80$ marbles of the same size respectively, some of which are black. In box $A$ there are $15$ black marbles. We select a box at random and then take a marble from that box, again at random. The probability to obtain a black marble this way is $\frac{101}{600}$. What is the greatest possible number of black marbles in box $C$?