Question

some farmers were monitoring the population of roe deer on their land. first, the farmers marked 92 roe deer. later, the farmers counted a total of 290 roe deer, of which 29 were marked. to the nearest whole number, what is the best estimate for the roe deer population?

Explanation:

Step1: Set up proportion

Let \( N \) be the total population. The proportion of marked deer in the second count should be equal to the proportion of marked deer in the total population. So \(\frac{29}{290}=\frac{92}{N}\)

Step2: Solve for \( N \)

Cross - multiply: \( 29N = 92\times290 \)
First, calculate \( 92\times290=92\times(300 - 10)=92\times300-92\times10 = 27600-920 = 26680 \)
Then, \( N=\frac{26680}{29}\approx920 \)

Answer:

\( 920 \)