2023 AMC 8

Complete problem set with solutions and individual problem pages

Problem 5 Easy

A lake contains 250 trout, along with a variety of other fish. When a marine biologist catches and releases a sample of 180 fish from the lake, 30 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?

  • A.

    1250

  • B.

    1500

  • C.

    1750

  • D.

    1800

  • E.

    2000

Answer:B

Note that

\frac{\text{number of trout}}{\text{total number of fish}} = \frac{30}{180} = \frac16.

So, the total number of fish is 6 times the number of trout. Since the lake contains 250 trout, there are 250\cdot6=\boxed{\textbf{(B)}\ 1500} fish in the lake.

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