a tilapia fish hatchery selectively releases fish when the populations have increased beyond a certain…

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?

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?

Answer

Explanation:

Step1: Set up proportion

Let $x$ be the total fish population. The proportion is $\frac{\text{marked fish in first - catch}}{\text{total first - catch}}=\frac{\text{marked fish in second - catch}}{\text{total second - catch}}$, so $\frac{780}{x}=\frac{72}{1200}$.

Step2: Cross - multiply

Cross - multiplying gives us $72x = 780\times1200$.

Step3: Solve for $x$

First, calculate $780\times1200 = 936000$. Then $x=\frac{936000}{72}=13000$.

Answer:

13000