Pregunta
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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?

Ask by French George. in the United States
Feb 03,2025

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Santiago's car travels 9.2 miles less per gallon than Grayson's car.

Solución

To determine how many miles less Santiago's car travels on one gallon of gas compared to Grayson's car, follow these steps: 1. **Calculate Santiago's Mileage:** The equation given is \( y = 31.9x \), where \( y \) is the number of miles and \( x \) is the number of gallons. This means Santiago's car travels **31.9 miles per gallon**. 2. **Calculate Grayson's Mileage:** Grayson uses 8 gallons of gas to drive 328.8 miles. \[ \text{Mileage} = \frac{\text{Total Miles}}{\text{Gallons Used}} = \frac{328.8}{8} = 41.1 \text{ miles per gallon} \] 3. **Determine the Difference:** Subtract Santiago's mileage from Grayson's mileage to find the difference per gallon. \[ 41.1 \text{ mpg} - 31.9 \text{ mpg} = 9.2 \text{ miles per gallon} \] **Conclusion:** Santiago's car travels **9.2 miles less per gallon** than Grayson's car. **Answer:** Santiago’s car travels 9.2 miles less per gallon than Grayson’s car.

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Beyond the Answer

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.

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