Question

Scientists want to know the total trout population in a part of Lake Michigan. They tagged and released 200 trouts back into the wild. Later, they found 60 trouts in that same part of Lake Michigan, 10 of which were tagged. Estimate the total trout population in that part of Lake Michigan to the nearest whole number.

Answer 1

The estimate would be 1200.

We will set up a proportion for this.  10 out of 60 of the sample were tagged, so that is the first ratio.  The 200 that were tagged would be in the numerator of the second ratio (10 was the portion tagged, and 200 is the portion tagged, so they both go on top).  We do not know the total number so we use a variable:

10/60 = x/200

Cross multiply:

10*x = 60*200
10x = 12000

Divide both sides by 10:
10x/10 = 12000/10
x = 1200