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Chapter 6: Problem 114

To estimate the number of bass in a lake, wildlife biologists tagged 50 bass and released them in the lake. Later they netted 108 bass and found that 27 of them were tagged. Approximately how many bass are in the lake?

Short Answer

Expert verified
There are approximately 200 bass in the lake.

Step by step solution

01

Identify the Known Ratios

We know two important ratios. The first is the ratio of tagged bass to the total number of bass the biologists netted, which is 27 out of 108, or \( \frac{27}{108} \). The second is the ratio of tagged bass to the total number of bass in the lake, which is 50 out of X, with X being what we are trying to identify.
02

Set Up an Equation

Since the ratios should be equal, the equation becomes \( \frac{27}{108} = \frac{50}{X} \)
03

Solve for X

To solve for X, cross-multiply and solve gets \( 27X = 108*50 \). Solving this equation gives \(X = \frac{108*50}{27}\).

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