Question

a country in africa is trying to restore its zebra population and is carefully keeping track of how many zebras are in the area. to do so, local wildlife authorities put tags on 140 zebras and release them. later, they corral 450 zebras; among those zebras, 30 are tagged. to the nearest whole number, what is the best estimate for the zebra population?

Explanation:

Step1: Set up proportion

Let $N$ = total population. The ratio of tagged zebras in the sample equals the ratio of tagged zebras in the population:
$$\frac{30}{450} = \frac{140}{N}$$

Step2: Simplify left fraction

Reduce $\frac{30}{450}$ to simplest form:
$$\frac{1}{15} = \frac{140}{N}$$

Step3: Solve for $N$

Cross-multiply to isolate $N$:
$$N = 140 \times 15$$
$$N = 2100$$

Answer:

2100