Adrian's lawn mower runs on a fuel combination of oil and gasoline. The table shows the amount of of oil, l, Adrian mixed with the amount of gasoline, g, when he filled the fuel tank.

Question

Amount of
Oil, l
(in liters) Amount of
Gasoline, g
(in liters)
0.05 1.6
0.10 3.2
0.15 4.8
0.2 6.4
0.25 8

Which equation represents the proportional relationship between the amounts of oil and gasoline used to make the fuel for the lawnmower?
A. l = g + 3.2

B. g = 32l

C. l = 32g

D. g = l + 3.2

Answer 1

To find the proportional relationship between the amounts of oil (l) and gasoline (g), we can look for a ratio or constant that connects the two.

From the data provided, we can calculate the ratio of gasoline to oil for each pair:

• For \( l = 0.05 \), \( g = 1.6 \): the ratio \( \frac{g}{l} = \frac{1.6}{0.05} = 32 \)
• For \( l = 0.10 \), \( g = 3.2 \): the ratio \( \frac{g}{l} = \frac{3.2}{0.10} = 32 \)
• For \( l = 0.15 \), \( g = 4.8 \): the ratio \( \frac{g}{l} = \frac{4.8}{0.15} = 32 \)
• For \( l = 0.20 \), \( g = 6.4 \): the ratio \( \frac{g}{l} = \frac{6.4}{0.20} = 32 \)
• For \( l = 0.25 \), \( g = 8.0 \): the ratio \( \frac{g}{l} = \frac{8.0}{0.25} = 32 \)

The ratio \( \frac{g}{l} = 32 \) suggests that the amount of gasoline is 32 times the amount of oil. Therefore, we can express the relationship as:

\[ g = 32l \]

This corresponds to option B:

B. g = 32l