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To determine the jackrabbit population in a wildlife preserve, researchers tagged $67$ jackrabbits. Later, they counted $310$ jackrabbits. Out of the jackrabbits they counted, $31$ had tags. To the nearest whole number, what is the best estimate for the jackrabbit population?

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Estimate population size using proportions

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Q. To determine the jackrabbit population in a wildlife preserve, researchers tagged

67

jackrabbits. Later, they counted

310

jackrabbits. Out of the jackrabbits they counted,

31

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

Set up proportion: Step $1$ : Set up the proportion based on the information given. $\newline$ We know: $\newline$ - Marked jackrabbits found: $31$ $\newline$ - Total jackrabbits counted: $310$ $\newline$ - Total jackrabbits marked: $67$ $\newline$ Let $p$ be the estimated jackrabbit population. $\newline$ We set up the proportion: $\newline$ $\frac{31}{310} = \frac{67}{p}$
Solve proportion: Step $2$ : Solve the proportion by cross-multiplying to find $p$ . Cross-multiplying gives: $31 \times p = 67 \times 310$ $31p = 20770$
Isolate and solve: Step $3$ : Divide both sides by $31$ to isolate $p$ and solve for the estimated population. $\newline$ $p = \frac{20770}{31}$ $\newline$ $p = 670$

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