Question

to determine the number of trout in a lake, a conservationist catches 202 trout, tags them, and releases them. later 106 trout are caught, and it is found that 82 of them are tagged. estimate how many there are in the lake.
the approximate number of trout is
(round to the nearest whole number as needed.)

Explanation:

Step1: Set up proportion

Let $x$ be the total number of trout in the lake. The proportion is $\frac{202}{x}=\frac{82}{106}$.

Step2: Cross - multiply

We get $82x = 202\times106$.

Step3: Calculate the right - hand side

$202\times106=21412$. So, $82x = 21412$.

Step4: Solve for $x$

$x=\frac{21412}{82}\approx261.12$.

Step5: Round to the nearest whole number

Rounding $261.12$ to the nearest whole number gives $261$.

Answer:

$261$