1993 AIME Problem 3

The table below displays some of the results of last summer’s Frostbite Falls Fishing Festival, showing how many contestants caught n fish for various values of n.

\begin{aligned} &\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline n & 0 & 1 & 2 &3 &\cdots& 13 & 14 & 15 \\ \hline \begin{array}{c} \text { number of contestants } \\ \text { who caught } n \text { fish } \end{array} & 9 & 5 & 7 & 23 &\cdots& 5 & 2 & 1\\ \hline \end{array} \end{aligned}

In the newspaper story covering the event, it was reported that
a) the winner caught 15 fish;
b) those who caught 3 or more fish averaged 6 fish each;
c) those who caught 12 or fewer fish averaged 5 fish each.
What was the total number of fish caught during the festival?