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Cara is a farmer who has noticed a lot of snails eating her vegetables and wants to estimate the number of snails on her land. She sets up traps and catches $38$ snails. She marks the snails, releases them, and replaces the traps. Later, when she returns to the traps, she counts $170$ snails, $17$ of which are marked. To the nearest whole number, what is the best estimate for the snail population?

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Estimate population size using proportions

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Q. Cara is a farmer who has noticed a lot of snails eating her vegetables and wants to estimate the number of snails on her land. She sets up traps and catches

38

snails. She marks the snails, releases them, and replaces the traps. Later, when she returns to the traps, she counts

170

snails,

17

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

Set up proportion: Step $1$ : Set up the proportion based on the capture-recapture method. Cara marked and released $38$ snails, then later captured $170$ snails, $17$ of which were marked. We set up the proportion: $\frac{\text{marked snails in second capture}}{\text{total snails in second capture}} = \frac{\text{marked snails released}}{\text{total snail population}}$ $\frac{17}{170} = \frac{38}{p}$
Solve for p: Step $2$ : Solve for p using cross multiplication. $\newline$ Cross multiply to find p: $\newline$ $17 \times p = 38 \times 170$ $\newline$ $17p = 6460$
Isolate $p$ : Step $3$ : Divide both sides by $17$ to isolate $p$ . $\newline$ $p = \frac{6460}{17}$ $\newline$ $p = 380$

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