Question

the table shows two samples of fish from a pond. if 400 fish are in the pond, which proportion represents the average number of bass you would expect to live in the pond?
trout: 3 (sample 1), 5 (sample 2)
catfish: 9 (sample 1), 9 (sample 2)
bass: 8 (sample 1), 6 (sample 2)
all fish: 20 (sample 1), 20 (sample 2)
options:
$\frac{14}{20}=\frac{x}{400}$
$\frac{7}{20}=\frac{400}{x}$
$\frac{7}{20}=\frac{x}{400}$
$\frac{20}{40}=\frac{x}{400}$

Explanation:

Step1: Calculate average number of bass in samples

The number of bass in sample 1 is 8 and in sample 2 is 6. The average number of bass in the two - sample is $\frac{8 + 6}{2}=7$. The total number of fish in each sample is 20.

Step2: Set up proportion

We use the proportion of the average number of bass in the samples to the total number of fish in the samples equal to the proportion of the expected number of bass in the pond ($x$) to the total number of fish in the pond (400). So the proportion is $\frac{7}{20}=\frac{x}{400}$.

Answer:

$\frac{7}{20}=\frac{x}{400}$