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 fish for various values of
.
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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
Suppose that the number of fish is and the number of contestants is
. Of those which caught 3 or more fish (
did that),
fish were caught. Since they averaged 6 fish,
. Similarily, of those which caught 12 or fewer fish averaged 5 fish per person, so
. Solving the two equation system, we find that
and
, the answer.
See also
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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