At a corner gas​ station, the revenue R varies directly with the number g of gallons of gasoline sold. If the revenue is ​$55.20 when the number of gallons sold is 12​, find a linear equation that relates revenue R to the number g of gallons of gasoline. Then find the revenue R when the number of gallons of gasoline sold is 8.5.


The problem states that revenue $ R $ varies directly with the number of gallons $ g $ of gasoline sold. This means we can express the relationship as a linear equation:

\[
R = k \cdot g
\]

where $ k $ is the constant of proportionality.

### Step 1: Find the constant $ k $
We are given that the revenue is $55.20 when the number of gallons sold is 12. Plugging these values into the equation:

\[
55.20 = k \cdot 12
\]

Solving for $ k $:

\[
k = \frac{55.20}{12} = 4.60
\]

Thus, the linear equation that relates revenue $ R $ to the number of gallons $ g $ of gasoline sold is:

\[
R = 4.60 \cdot g
\]

### Step 2: Find the revenue when $ g = 8.5 $
Now, we can use the equation to find the revenue when 8.5 gallons of gasoline are sold:

\[
R = 4.60 \cdot 8.5 = 39.10
\]

So, the revenue is $39.10 when 8.5 gallons of gasoline are sold.

Would you like more details or have any questions?

Here are 5 related questions to expand this topic:
1. How would the equation change if the revenue per gallon increased?
2. How do you interpret the slope of the equation $ R = 4.60 \cdot g $?
3. What happens to the revenue if the number of gallons sold doubles?
4. Can you graph the equation and interpret its meaning visually?
5. How would you calculate the number of gallons needed to reach $100 in revenue?

**Tip:** Always check the units to ensure your calculations maintain consistency, especially in direct variation problems.

At a corner gas station, the revenue R varies directly with the number g of gallons of gasoline sold. If the revenue is $55.20 when the number of gallons sold is 12, find a linear equation that relates revenue R to the number g of gallons of gasoline. Then find the revenue R when the number of gallons of gasoline sold is 8.5.

Discover how to calculate revenue based on the number of gallons sold using direct variation. Learn how the equation R = 4.60 * g is derived, and find the revenue when 8.5 gallons are sold. This math problem is perfect for students in Grades 8-10 who are learning about linear equations and direct proportionality.

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