recently, there has been an epidemic among prairie dogs. clayton is a scientist who studies how diseases…

recently, there has been an epidemic among prairie dogs. clayton is a scientist who studies how diseases spread and wants to estimate the size of a particular prairie dog town. first he catches 200 prairie dogs and tags them. these prairie dogs are then released, and at a later date, 680 prairie dogs are caught. among these prairie dogs, 85 are tagged. to the nearest whole number, what is the best estimate for the prairie dog population?

recently, there has been an epidemic among prairie dogs. clayton is a scientist who studies how diseases spread and wants to estimate the size of a particular prairie dog town. first he catches 200 prairie dogs and tags them. these prairie dogs are then released, and at a later date, 680 prairie dogs are caught. among these prairie dogs, 85 are tagged. to the nearest whole number, what is the best estimate for the prairie dog population?

Answer

Explanation:

Step1: Set up the proportion

Let $x$ be the total prairie - dog population. The proportion is based on the fact that the ratio of tagged dogs in the first sample to the total population is equal to the ratio of tagged dogs in the second sample to the size of the second sample. So, $\frac{200}{x}=\frac{85}{680}$.

Step2: Cross - multiply

Cross - multiplying gives us $85x = 200\times680$.

Step3: Calculate the right - hand side

$200\times680=136000$. So, the equation becomes $85x = 136000$.

Step4: Solve for $x$

Divide both sides of the equation by 85: $x=\frac{136000}{85}=1600$.

Answer:

1600