Question

writing a proportion
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?
\\(\frac{14}{20} = \frac{x}{400}\\)
\\(\frac{7}{20} = \frac{400}{x}\\)
\\(\frac{7}{20} = \frac{x}{400}\\)
\\(\frac{20}{40} = \frac{x}{400}\\)
(table:

	sample 1	sample 2
catfish	9	9
bass	8	6
all fish	20	20

)

Explanation:

Step1: Calculate average bass per sample

First, find the total number of bass in both samples: $8 + 6 = 14$. Then find the average number of bass per sample: $\frac{14}{2} = 7$.

Step2: Set up the proportion

The average ratio of bass to total fish in a sample is $\frac{7}{20}$. Let $x$ be the expected number of bass in 400 total fish. The proportion equates the sample ratio to the pond ratio: $\frac{7}{20} = \frac{x}{400}$.

Answer:

$\frac{7}{20} = \frac{x}{400}$ (the third option)