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This problem trains for: SAT-I, AMC-8, GMAT.

A fish farm wants to determine the number of fish in one of its ponds. For this purpose, they take some sample catches from the pond, catching a total of 1700 fish. They decide to relocate 300 of them to another pond. The remaining fish are tagged and released. After a few days, another sample catch is done. Among the 1200 fish that are caught, tags were found on 230 of them. How many fish were there in the pond initially? (round to the nearest hundred)

Assuming the tagged fish swam around and distributed themselves randomly within the pond, we have the following proportionality:

Size of sampleNumber of tagged individuals
x1400
1200230

Therefore,

equation

Since 300 individuals had been relocated, it is plausible to assume that there were 7600 fish in the pond initially.