SOLUTION: : A farmer wants to know how many fish there are in his dam. He took out 200 fish and tagged each of them, with a coloured sign. He put the tagged fish back in the dam and let them

Question 875796: : A farmer wants to know how many fish there are in his dam. He took out 200 fish and tagged each of them, with a coloured sign. He put the tagged fish back in the dam and let them get mixed with the others. On the second day, he took out 250 fish in a random manner, and found that 25 of them were tagged. Estimate how many fish are in the dam.
Question options:

450

800

2000

2175 I did this but it is wrong

4500

Answer by josgarithmetic(39618) (Show Source): You can put this solution on YOUR website!
Two equal ratios, a proportion.

Let p = the dam population.
200 fish were tagged. This gives total/tagged.

The recheck was total/tagged.

The proportion is ; solve for p.

"Not make sense...", the explanation.
After tagging the fish, the dam contains p fish, and 200 of them are tagged. This is a ratio of p/200, and the units of this ratio are Total Fish to Tagged Fish.
Upon catching fish to recheck what happened, 250 fish were caught and the number of fish found with tags was 25 fish. This ratio is 250/25 and the units for this is Fish to Tagged fish.
THESE RATIOS ARE EXPECTED TO BE EQUAL. This means . The original collection of tagged fish put into the dam became uniformly diluted, hypothetically. Solve for p.
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