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In order to estimate the number of monkeys living in a certain rain forest, Wayne catches $35$ monkeys, marks them, and releases them. Later, Wayne catches $180$ monkeys and notes that $15$ of them are marked. To the nearest whole number, what is the best estimate for the monkey population?

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Estimate population size using proportions

Full solution

Q. In order to estimate the number of monkeys living in a certain rain forest, Wayne catches

35

monkeys, marks them, and releases them. Later, Wayne catches

180

monkeys and notes that

15

of them are marked. To the nearest whole number, what is the best estimate for the monkey population?

Set up proportion: Step $1$ : Set up the proportion based on the capture-recapture method.
Solve proportion: Step $2$ : Solve the proportion by cross-multiplying to find $M$ .
Isolate and solve: Step $3$ : Divide both sides by $15$ to isolate $M$ and solve for the estimated population.

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