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?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Note that . This means that a sixth of the fish in the lake are trout, or in other words, the total number of fish is times the number of trout. Therefore, there are fish in the lake. Thus, is the correct answer.
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions