Question

The New Mexico Division of Fish and Wildlife keeps track of the silvery minnow population in the Rio Grande River. They tagged 54 silvery minnows and released them. A week later, they captured 62 silvery minnows, including 12 tagged silvery minnows. What is a good estimate of the silvery minnow population in the Rio Grande River?

Answer 1

Answer:

279 silvery minnow

Step-by-step explanation:

Number of Silvery Minnows initially tagged = 54

Number of minnows captured = 62

Number of tagged minnows in captured ones = 12

Remember that in the very beginning there were no tagged minnows. 54 minnows were captured, tagged and released. This means, there are total 54 tagged minnows in the entire population. Lets say there are x number of minnows in total.

So, in x minnows, 54 are tagged ones.

When 62 minnows are captured, only 12 are tagged ones and remaining are un-tagged. Since, the minnows were randomly captured, we can develop a proportion from this case to estimate the total population of minnows in the Rio Grande River.

Ratio of tagged minnows to total population must be equal to the ratio of captured tagged minnows in total captured minnows.

i.e.

$54 : x = 12 : 62\\\\ \frac{54}{x} = \frac{12}{62}\\\\ 62(54)=12x\\ \\ x = 279$

This means, there were 279 silvery minnows in the Rio Grande River.