Question

a tilapia fish hatchery selectively releases fish when the populations have increased beyond a certain target level. in order to estimate the current fish population, workers at the hatchery catch 780 fish and mark them with special paint. then a little while later, they catch 1,200 fish, among which 72 are marked. to the nearest whole number, what is the best estimate for the fish population?

Explanation:

Step1: Set up proportion

Let $N$ = total population. The ratio of marked fish in the second catch equals the ratio of marked fish to total population:
$\frac{72}{1200} = \frac{780}{N}$

Step2: Solve for $N$

Cross-multiply to isolate $N$:
$N = \frac{780 \times 1200}{72}$

Step3: Calculate the value

Compute the numerator first, then divide:
$N = \frac{936000}{72} = 13000$

Answer:

13000