Question 894859: This question is in the ratios & proportions section of the book. The problem is that there are no instructions or examples. I would be grateful if I could get a detailed answer so that I know how to complete the other questions like this.
Set up the proportion:
Set up the two ratios and write your equation, choosing an appropriate variable for the bear population.
Bear population. To estimate the size of the bear population on the Keweenaw Peninsula, conservationists captured, tagged, and released 50 bears. One year later, a random sample of 100 bears included only 2 tagged bears. What is the conservationist's estimate of the size of the bear population?
Thank you!
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! a random sample of 50 bears were tagged and released.
one year later they took a random sample of 100 bears.
2 of them were tagged and the rest were not.
all things being equal, they determined that the number of bears must have been 50 / 2 * 100 = 2500.
here's how they did it and why.
they took a sample of 50 and tagged them all.
this 50 was out of an unknown number of bears in the population.
they assigned x to represent the number of bears in the population.
they got a ratio of 50 / x.
that's 50 tagged bears out of x bears.
when they took another sample of 100 bears and found that 2 were tagged, they now had a sample where they knew the number of tagged bears in relationship to the number of total bears.
all things being equal, this sample should have the same ratio as the original sample.
the original sample was 50/x
this sample was 2/100
they set the ratios equal to each other and they got 50/x = 2/100
they cross multiplied to get 2x = 50*100
they divided both sides of the equation by 2 to get x = 50*100/2.
they solved for x to get x = 2500.
they estimated that the bear population was somewhere around 2500 based on this sample.
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