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Flora is monitoring the population of red kangaroos in the deserts of Australia. Flora catches 20 red kangaroos and releases them. A little while later, a helicopter pilot takes an aerial photograph of 450 red kangaroos, 10 of which are marked. What is the best estimate for the red kangaroo population?

The ratio of marked red kangaroos to total red kangaroos should be about the same in both the sample population and the overall population. You know how many red kangaroos were in the sample and how many of those were marked. You also know the total number of marked red kangaroos.

Set up a proportion.

 number of marked red kangaroos counted ____________________________________ total number of red kangaroos counted
=
 total number of marked red kangaroos _______________________________ estimate of red kangaroo population

Plug in the numbers you know and solve for the red kangaroo population, p.

$\frac{10}{450}=\frac{20}{p}$

 10p = 20 × 450 Find the cross products 10p = 9,000 Simplify p = 900 Divide both sides by 10

The best estimate for the red kangaroo population is 900
.