Two friends, Grayson and Santiago, had just bought their first cars. The equation \( y=31.9 x \) 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. How many miles less does Santiago's car travel on one gallon of gas than Grayson's car?
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To find out how many miles Santiago's car travels on one gallon of gas, we need to take the equation \( y = 31.9x \) and use \( x = 1 \) gallon. So, for Santiago’s car: \[ y = 31.9 \times 1 = 31.9 \text{ miles} \] Next, we need to determine how many miles Grayson’s car travels per gallon. Grayson drives 328.8 miles with 8 gallons of gas, so we find the miles per gallon (MPG) for Grayson: \[ \text{MPG} = \frac{328.8 \text{ miles}}{8 \text{ gallons}} = 41.1 \text{ miles per gallon} \] Now, we will find the difference in miles per gallon between Grayson’s and Santiago’s cars: \[ \text{Difference} = 41.1 - 31.9 = 9.2 \text{ miles} \] Therefore, Santiago's car travels 9.2 miles less on one gallon of gas than Grayson’s car.