To determine how many miles Luke would drive on 13 gallons, we first need to identify the constant of variation in the relationship between the number of gallons used and the number of miles driven.
The variation formula can be expressed as:
\[ \text{Miles} = k \times \text{Gallons} \]
where \( k \) is the constant of variation.
We can use the provided values to find \( k \). Let's take the first set of data:
- For 9 gallons: 171 miles \[ k = \frac{\text{Miles}}{\text{Gallons}} = \frac{171}{9} = 19 \]
Now let's check the other data points to confirm that \( k \) is consistent:
-
For 19 gallons: 361 miles \[ k = \frac{361}{19} = 19 \]
-
For 33 gallons: 627 miles \[ k = \frac{627}{33} = 19 \]
Since \( k \) is consistently 19 across all data points, we can use this to find out how many miles Luke would drive with 13 gallons:
\[ \text{Miles} = k \times \text{Gallons} = 19 \times 13 = 247 \]
Thus, Luke would drive 247 miles on 13 gallons.
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