estimate how many rabbits?

[tmoria0]

Q. In a forest, the warden wants to estimate the number of rabbits. He catches and marks 140 rabbits and releases them. The next day he catches 80 rabbits and finds 23 of them are marked.​
Estimate the number of rabbits in the forest.

OK, I know there are at least 140 + (80 - 23) = 197 rabbits but don't think this is the correct answer.

If I take the percentage of the marked/unmarked rabbits caught the second day I get (23/80)*100 = 28.75%
So I think if I say that 28.75% of the population are marked, and I know this figure is 140 rabbits then
the total population is (140/28.75)*100 = 487 rabbits.

Is this 2nd attempt correct? If so could someone give an explanation as to why because I'm sort of flying by the seat of my pants here.

Thanks for your time

Terry

 

[HallsofIvy]

Yes, that is correct. The argument is that, if we call the number of rabbits in the forest "X", then, after the marking, the ratio of rabbits marked is \(\displaystyle \frac{140}{X}\). Assuming we have caught the rabbits we marked and released from all around the forest and the same for the second group, it is reasonable to think that the fraction will be the same: \(\displaystyle \frac{140}{X}= \frac{23}{80}\) x that (140)(80)= 23X which has X= 486.9 as solution.