a worker at a local aquarium is instructed to estimate the population of sardines in the tank. he catches…

a worker at a local aquarium is instructed to estimate the population of sardines in the tank. he catches 180 sardines, marks them with special paint, and returns them to the tank. then he catches 420 sardines and finds that 14 of them are marked. to the nearest whole number, what is the best estimate for the sardine population?

a worker at a local aquarium is instructed to estimate the population of sardines in the tank. he catches 180 sardines, marks them with special paint, and returns them to the tank. then he catches 420 sardines and finds that 14 of them are marked. to the nearest whole number, what is the best estimate for the sardine population?

Answer

Explanation:

Step1: Set up the proportion

Let $x$ be the total sardine population. The ratio of marked sardines in the first - catch to the total population should be equal to the ratio of marked sardines in the second - catch to the size of the second - catch. So we have the proportion $\frac{180}{x}=\frac{14}{420}$.

Step2: Cross - multiply

Cross - multiplying gives us $14x = 180\times420$.

Step3: Calculate the right - hand side

$180\times420=75600$. So the equation becomes $14x = 75600$.

Step4: Solve for $x$

Dividing both sides of the equation by 14, we get $x=\frac{75600}{14}=5400$.

Answer:

5400