a man captures 120 fish and releases back in lake, a week later he catches 175 fish. only 8 have tags, how many fish are in pond

Question

a man caputures 120 fish and release them back in the lake.  a week later he resets and catches 175 fish.  of those 8 have tags, assuming the man has captured a random of the fish how many fish are in the pond?

Answer 1

Let X = number of fish in the pond.  

 

8 of the 175 caught fish have tags.  

 

120 of the X fish in the lake have tags. 

 

So the ratio is  8:175 :: 120:X

 

In fraction form this is 

 

(8/175) = (120/X)

 

Cross multiply to get 

 

8X = (175)(120)

X = (175)(120/8) = (175)(15) = 2625 fish in the pond (before he caught the 175)