Question

to determine the number of trout in a lake, a conservationist catches 187 trout, tags them and throws them back into the lake. later, 40 trout are caught, 10 of them are tagged. how many trout would the conservationist expect to be in the lake? the conservationist would expect that there are trout in the lake.

Explanation:

Step1: Set up proportion

Let $x$ be the total number of trout in the lake. The ratio of tagged trout in the first - catch to the total number of trout in the lake should be equal to the ratio of tagged trout in the second - catch to the number of trout in the second - catch. So we have the proportion $\frac{187}{x}=\frac{10}{40}$.

Step2: Cross - multiply

Cross - multiplying gives us $10x = 187\times40$.

Step3: Solve for $x$

First, calculate $187\times40 = 7480$. Then, $x=\frac{7480}{10}=748$.

Answer:

748