Question 31223
Hello!
When they returned on Fenruary 1, they found that 8 out of 400 fish were tagged. Therefore, a good estimate would be to say that, in the lake, 8 out of every 400 fish are tagged. Or equivalently ({{{8/400*100 = 2}}}) 2% of all the fish in the lake are tagged.

We know that 2% of all the fish in the lake are tagged. We also know that 500 fish are tagged. So we conclude that 500 is 2% of the total number of fish in the lake. So, calling X to the total number of fish, we have the equation:

{{{(2/100)X = 500}}}
Solving for X:
{{{X = 500*(100/2) = 25000}}}

Hence there are 25,000 fish in the lake.


I hope this helps!
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