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

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?

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.