Question

A teacher driving to a conference in a school van records the number of gallons of gas used and the number of miles traveled.

Complete the table to show the case where there is a proportional relationship between the number of gallons of gas used by the school van and the number of miles traveled.

Gallons of GasMiles Traveled00411010

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330

Answer 1

To complete the table showing a proportional relationship between the number of gallons of gas used and the number of miles traveled, we need to establish a consistent ratio. A proportional relationship means that as the number of gallons increases, the number of miles traveled increases at a constant rate.

Let's denote the number of gallons of gas used by \( g \) and the number of miles traveled by \( m \). From the information provided in the table, we know:

- For 0 gallons of gas, 0 miles are traveled: \( (0, 0) \)
- For 4 gallons of gas, 110 miles are traveled: \( (4, 110) \)
- For 10 gallons of gas, we need to find out how many miles are traveled: \( (10, ?) \)
- To find the relationship consistently, let's also include the 3 gallons case where we have traveled 30 miles: \( (3, 30) \)

Now, let's find the constant rate (miles per gallon) using the known points.

From \( (4, 110) \):
- \( 110 \text{ miles} / 4 \text{ gallons} = 27.5 \text{ miles per gallon} \)

Now, we can use this rate to fill in the table.

**Calculating for 3 gallons:**
- \( 3 \text{ gallons} \times 27.5 \text{ miles/gallon} = 82.5 \text{ miles} \)

**Calculating for 10 gallons:**
- \( 10 \text{ gallons} \times 27.5 \text{ miles/gallon} = 275 \text{ miles} \)

Here is the completed table:

| Gallons of Gas | Miles Traveled |
|----------------|----------------|
| 0 | 0 |
| 3 | 82.5 |
| 4 | 110 |
| 10 | 275 |

This table signifies a proportional relationship between gallons of gas and miles traveled, with a consistent ratio of 27.5 miles per gallon.