Problem:
A lake contains trout, along with a variety of other fish. When a marine biologist catches and releases a sample of fish from the lake, are identified as trout. Assume that the ratio of trout to the total number of fish is the same in both the sample and the lake. How many fish are there in the lake?
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Solution:
In the sample, the trout make up of the number of fish caught. The trout-to-fish ratio is the same in both the sample and the lake, so the trout in the lake must make up of the total. Therefore there are fish in the lake.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions