SOLUTION: One way to estimate how many fish are in a lake is to use the capture-recapture method. Suppose you capture 100 fish, tag them, then release them back in to the lake. Later, you ca

Algebra ->  Percentage-and-ratio-word-problems -> SOLUTION: One way to estimate how many fish are in a lake is to use the capture-recapture method. Suppose you capture 100 fish, tag them, then release them back in to the lake. Later, you ca      Log On


   

Question 70714: One way to estimate how many fish are in a lake is to use the capture-recapture method. Suppose you capture 100 fish, tag them, then release them back in to the lake. Later, you capture 100 fish again, and count 12 that are tagged. Now assume the the ratio of tagged to untagged fish in the same in your sample as in the entire lake and estimate the number of fish in the lake.
Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
You have released 100 tagged fish into the pond. You must assume these tagged fish distribute
themselves randomly and evenly throughout the pond. When you pull 100 fish out of the pond
you find that 12 of them are tagged.
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There are now several ways you can look at this. Since you know there are 100 tagged fish
in the pond, how many groups of 100 fish will you have to remove to recapture all 100 of the
tagged fish. At 12 tagged fish per group you will have to haul in 100%2F12+=+8.33 groups.
And at 100 fish per group this translates to a total of 833 fish in the pond.
.
Another way to look at it is by proportion. Of every 100 fish removed from the pond, 12 of
them are tagged. The ratio of 100 fish to 12 tagged fish should reflect the the composition
of the total pond. Again you know that there are 100 total tagged fish in the pond. Call the
total fish population F. You can then set up the proportion:
.
100%2F12+=+F%2F100
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Solve this by cross multiplying the numerator on one side by the denominator on the other
side, and do this for each numerator, the one on the left side and the one on the right
side. The result will be:
.
100%2A100+=+12%2AF
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Solve this by dividing both sides by 12 to get:
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F+=+%28100%2A100%29%2F12+=+833
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Again this tells you that there are about 833 fish in the pond.
.
And a final way you could view it is by saying that out of the 100 fish you take from the
pond 12% are tagged. Therefore you can assume that 12% of the total fish population
(designated as F) are tagged. But we know that the total number of tagged fish is 100.
Therefore, we can write:
.
0.12%2AF+=+100
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where 0.12 is the decimal equivalent of 12%. Solve this equation by dividing both sides
by 0.12 and you will again that the total fish population (F) is approximately 833 fish.
.
Hopefully one or more of these viewpoints will help you to see how to do this problem.