# Problem #244

 244 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 $n\,$. $\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline n & 0 & 1 & 2 & 3 & \dots & 13 & 14 & 15 \\ \hline \text{number of contestants who caught} \ n \ \text{fish} & 9 & 5 & 7 & 23 & \dots & 5 & 2 & 1 \\ \hline \end{array}$ 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? This problem is copyrighted by the American Mathematics Competitions.
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• Reduce fractions to lowest terms and enter in the form 7/9.
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