A biologist catches 46 fish in a pond, tags them, and then releases them back into the pond. On a later visit to the pond, the biologist catches 20 fish, of which 8 are tagged. Which is the best estimate for the number of fish in the pond?

Question

A biologist catches 46 fish in a pond, tags them, and then releases them back into the pond. On a later visit to the pond, the biologist catches 20 fish, of which 8 are tagged.    Which is the best estimate for the number of fish in the pond?

anonymous · Answer

He catches 46 different fish one day. The next day he catches 20, but are the same fish he caught before. Do you have an idea where to start?

anonymous · Answer

but 8 are the same fish*****

anonymous · Answer

I'm not sure what you mean, the answers are either : 
A.66
B.115
C.368
D.920

anonymous · Answer

Well, to solve this we can use a method called Proportion in Lowest Terms.

anonymous · Answer

Okay.... So how do we do this?

anonymous · Answer

fish tagged and released = a
totalfish = t
 fish caught again with tags = b
fish caught again = c
$$\frac{ a }{ t } = \frac{ b }{ c }$$

anonymous · Answer

a = 46
b = 8
c = 20
t = ?
Solve for t

anonymous · Answer

Is it 920 ?

anonymous · Answer

46/t = 8/20  ==> $$\frac{ 46 }{ t }=\frac{ 2 }{ 5 }$$
$$46=\frac{ 2 }{ 5 }t$$
$$46(5)= 2t$$
$$t=\frac{ 46(5) }{ 2 }$$

anonymous · Answer

Oh, 115!

anonymous · Answer

Thanks!

anonymous · Answer

no problem