Two friends, Grayson and Santiago, had just bought their first cars. The equation y, equals, , 9, y=31.9x represents the number of miles, y that Santiago can drive his car for every x gallons of gas. Grayson uses 8 gallons of gas to drive 328.8 miles in his car.

Question

How many miles less does Santiago's car travel on one gallon of gas than Grayson's car?

Answer 1

To find out how many miles less Santiago's car travels on one gallon of gas compared to Grayson's car, we need to calculate the miles per gallon (mpg) for both cars.

Step 1: Calculate Grayson's miles per gallon.

Grayson drives 328.8 miles using 8 gallons of gas. Therefore, his miles per gallon can be calculated as follows:

\[ \text{Miles per gallon for Grayson} = \frac{\text{Total miles}}{\text{Total gallons}} = \frac{328.8 \text{ miles}}{8 \text{ gallons}} = 41.1 \text{ miles per gallon} \]

Step 2: Calculate Miles per gallon for Santiago's car using the given equation.

The equation provided for Santiago's miles is \( y = 31.9x \). Here, \( y \) represents the number of miles traveled and \( x \) represents the number of gallons of gas used. To find out how many miles Santiago can drive on one gallon, we substitute \( x = 1 \):

\[ y = 31.9 \times 1 = 31.9 \text{ miles per gallon} \]

Step 3: Find the difference in miles per gallon between Grayson and Santiago.

Now, we can calculate how many miles less Santiago's car travels per gallon compared to Grayson's:

\[ \text{Difference} = \text{Miles per gallon for Grayson} - \text{Miles per gallon for Santiago} = 41.1 - 31.9 = 9.2 \text{ miles} \]

Conclusion:

Santiago's car travels 9.2 miles less on one gallon of gas than Grayson's car.