a national park hires danny to estimate its antelope population. danny catches 117 antelope, tags them, and…

a national park hires danny to estimate its antelope population. danny catches 117 antelope, tags them, and releases them. then danny uses binoculars to observe a group of 255 antelope, 27 of which are tagged. to the nearest whole number, what is the best estimate for the antelope population?

a national park hires danny to estimate its antelope population. danny catches 117 antelope, tags them, and releases them. then danny uses binoculars to observe a group of 255 antelope, 27 of which are tagged. to the nearest whole number, what is the best estimate for the antelope population?

Answer

Explanation:

Step1: Set up proportion

Let $x$ be the total antelope population. The ratio of tagged - to - total in the first catch should equal the ratio of tagged - to - total in the second observation. So, $\frac{117}{x}=\frac{27}{255}$.

Step2: Cross - multiply

Cross - multiplying gives us $27x = 117\times255$. First, calculate $117\times255$: $117\times255=(100 + 10+7)\times255=100\times255+10\times255 + 7\times255=25500+2550 + 1785=29835$. So, $27x = 29835$.

Step3: Solve for $x$

Divide both sides of the equation $27x = 29835$ by 27: $x=\frac{29835}{27}=1105$.

Answer:

1105