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Oliver is monitoring the population of red kangaroos in the deserts of Australia. Oliver catches $55$ red kangaroos, tags them, and releases them. A little while later, a helicopter pilot takes an aerial photograph of $320$ red kangaroos, $11$ of which are marked. To the nearest whole number, what is the best estimate for the red kangaroo population?

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Estimate population size using proportions

Full solution

Q. Oliver is monitoring the population of red kangaroos in the deserts of Australia. Oliver catches

55

red kangaroos, tags them, and releases them. A little while later, a helicopter pilot takes an aerial photograph of

320

red kangaroos,

11

of which are marked. To the nearest whole number, what is the best estimate for the red kangaroo population?

Set up proportion: Step $1$ : Set up the proportion based on the capture-recapture method.
Solve for $K$ : Step $2$ : Solve the proportion by cross-multiplying to find $K$ .
Isolate $K$ : Step $3$ : Divide both sides by $11$ to isolate $K$ .

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