Question

A group of naturalists catch, tag and release 121 trout into a lake. The next day they catch and release 48 trout, of which 22 had been tagged. Using this ratio, how many trout would be estimated to be in the lake?

Answer 1

Answer:

264.

Step-by-step explanation:

Let x represent the number of trout in the lake.

We have been given that a group of naturalists catch, tag and release 121 trout into a lake. The next day they catch and release 48 trout, of which 22 had been tagged.

Using proportions, we will get:

$\frac{\text{Total trouts}}{\text{Tagged trouts}}=\frac{48}{22}$

$\frac{x}{121}=\frac{48}{22}$

$\frac{x}{121}*121=\frac{48}{22}*121$

$x=\frac{24}{11}*121$

$x=24*11$

$x=264$

Therefore, there would be approximately 264 trout in the lake.

Answer 2

264 trouts are estimated to be in the lake.

Using proportion, we write: Tagged trout/Total Trout

This becomes 22/48.

In order to use cross multiplication, we write another fraction using x, the total number of trout in the lake: 121/x.

Now we have 121/x=22/48.

We cross multiply.

121*48=22x.

(121*48)/22 becomes:

264.