Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses 8 gallons of gasoline to travel 216 miles.

Write a direct variation equation to represent the relationship. Use D for the distance the car travels (in miles) and for G amount of gasoline it uses (in gallons).

The relationship between distance \( D \) and the amount of gasoline \( G \) can be described using a **direct variation equation** of the form:

\[
D = k \cdot G
\]

Where:
- \( D \) is the distance traveled (in miles),
- \( G \) is the amount of gasoline used (in gallons),
- \( k \) is the constant of variation.

### Step 1: Determine the constant \( k \)
We know that the car uses 8 gallons of gasoline to travel 216 miles. Therefore, when \( G = 8 \), \( D = 216 \).

Substitute these values into the direct variation equation:

\[
216 = k \cdot 8
\]

Solve for \( k \):

\[
k = \frac{216}{8} = 27
\]

### Step 2: Write the direct variation equation
Now that we know \( k = 27 \), we can write the equation:

\[
D = 27 \cdot G
\]

This equation represents the relationship between the distance the car travels and the amount of gasoline it uses.

---

Do you want more details or have any questions?

Here are 5 related questions to expand on the topic:
1. How far would the car travel if it used 10 gallons of gasoline?
2. If the car traveled 135 miles, how many gallons of gasoline did it use?
3. Can you determine the fuel efficiency of the car in miles per gallon?
4. What would the constant \( k \) be if the car used 9 gallons of gasoline to travel 270 miles?
5. How would you adjust the equation if the car’s fuel efficiency changed over time?

**Tip:** In direct variation problems, the constant of variation \( k \) represents the rate of change, in this case, the car’s fuel efficiency in miles per gallon.

Suppose that the distance a car travels varies directly with the amount of gasoline it uses. A certain car uses 8 gallons of gasoline to travel 216 miles. Write a direct variation equation to represent the relationship. Use D for the distance the car travels (in miles) and G for the amount of gasoline it uses (in gallons).

Learn how to write a direct variation equation to represent the relationship between the distance a car travels and the amount of gasoline it uses. In this example, a car uses 8 gallons of gasoline to travel 216 miles, and we determine the equation D = 27G. This topic covers direct variation concepts and is suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation