1993 AIME Problems/Problem 3

Problem

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 $n\,$ .

$n\,$	$0\,$	$1\,$	$2\,$	$3\,$	$\dots\,$	$13\,$	$14\,$	$15\,$
$\mbox{number of contestants who caught }n\mbox{ fish}\,$	$9\,$	$5\,$	$7\,$	$23\,$	$\dots\,$	$5\,$	$2\,$	$1\,$

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?

Solution

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1993 AIME (Problems • Answer Key • Resources)
Preceded by Problem 2	Followed by Problem 4
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15
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1993 AIME Problems/Problem 3

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