The table shows the amount of seaweed powder, s, and the amount of fish powder, f, a factory uses to make different quantities of fertilizer.

Amount of
Seaweed Powder, s
(in pounds) Amount of
Fish Powder, f
(in pounds)
21.5 8.6
35.5 14.2
68.5 27.4
81.5 32.6
129.5 51.8

Which equation represents the proportional relationship between the amount of seaweed powder and the amount of fish powder in the fertilizer?

A. s = f + 2/5
B. f = 2/5s
C. s = 2/5f
D. f = s + 2/5

1 answer

To determine the proportional relationship between the amount of seaweed powder \( s \) and the amount of fish powder \( f \), we need to analyze the data points provided and find the relationship that holds true for all of them.

Let's first calculate the ratio between \( f \) and \( s \) for the given data points:

  1. \( f = 8.6 \) when \( s = 21.5 \) \[ \frac{f}{s} = \frac{8.6}{21.5} \approx 0.4 \]

  2. \( f = 14.2 \) when \( s = 35.5 \) \[ \frac{f}{s} = \frac{14.2}{35.5} \approx 0.4 \]

  3. \( f = 27.4 \) when \( s = 68.5 \) \[ \frac{f}{s} = \frac{27.4}{68.5} \approx 0.4 \]

  4. \( f = 32.6 \) when \( s = 81.5 \) \[ \frac{f}{s} = \frac{32.6}{81.5} \approx 0.4 \]

  5. \( f = 51.8 \) when \( s = 129.5 \) \[ \frac{f}{s} = \frac{51.8}{129.5} \approx 0.4 \]

From this analysis, we can see that the ratio \( \frac{f}{s} \) remains approximately constant at \( 0.4 \) for the data provided. Therefore, we can express this ratio as:

\[ f = \frac{2}{5}s \]

Thus, the equation that represents the proportional relationship between the amount of seaweed powder \( s \) and the amount of fish powder \( f \) is:

B. \( f = \frac{2}{5}s \).