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Scientists researching amphibians put tags on $36$ frogs in a wetland area. Later, the scientists captured $100$ frogs, of which $15$ had tags. To the nearest whole number, what is the best estimate for the frog population?

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Estimate population size using proportions

Full solution

Q. Scientists researching amphibians put tags on

36

frogs in a wetland area. Later, the scientists captured

100

frogs, of which

15

had tags. To the nearest whole number, what is the best estimate for the frog population?

Identify values, set up proportion: Step $1$ : Identify the given values and set up the proportion. $\newline$ We know: $\newline$ - Marked frogs counted: $15$ $\newline$ - Total frogs counted: $100$ $\newline$ - Total frogs marked: $36$ $\newline$ Let $p$ be the estimated frog population. $\newline$ Set up the proportion: $\newline$ $\frac{\text{marked frogs counted}}{\text{total frogs counted}} = \frac{\text{total frogs marked}}{\text{estimated frog population}}$ $\newline$ $\frac{15}{100} = \frac{36}{p}$
Solve by cross-multiplying: Step $2$ : Solve the proportion by cross-multiplying. $\newline$ Cross multiply to find $p$ : $\newline$ $15 \times p = 36 \times 100$ $\newline$ $15p = 3600$
Divide to isolate p: Step $3$ : Divide both sides by $15$ to isolate $p$ . $\frac{15p}{15} = \frac{3600}{15}$ $p = 240$

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