Question

a group of scientists tagged and released 27 otters as part of a research project. later, they counted 800 otters, 12 of which had tags. to the nearest whole number, what is the best estimate for the otter population?

Explanation:

Step1: Set up proportion

Let \( x \) be the otter population. The proportion of tagged otters in the sample should equal the proportion of tagged otters in the population. So, \(\frac{27}{x}=\frac{12}{800}\).

Step2: Cross - multiply and solve for \( x \)

Cross - multiplying gives \( 12x = 27\times800 \). First, calculate \( 27\times800 = 21600 \). Then, solve for \( x \) by dividing both sides by 12: \( x=\frac{21600}{12} \).

Step3: Calculate the value of \( x \)

\(\frac{21600}{12}=1800\).

Answer:

1800