Final answer:
To solve the question, two equations were created: x + y = 15 and 40x + 60y = 820. The solution for the number of gallons used on the highway is 11, which differs from the options provided; indicating a possible error in the options. The closest correct option, 8 gallons, is incorrect, the actual amount should be 11 gallons.
Step-by-step explanation:
To answer the question, we'll set up a system of equations based on the mileage information given. Let's denote the number of gallons used in the city as x and the number of gallons used on the highway as y. We know that x + y = 15, since the total amount of gas used is 15 gallons. We also know that 40x (the distance covered in the city) + 60y (the distance covered on the highway) equals the total distance traveled, which is 820 miles.
Therefore, we have the following system of equations:
- x + y = 15
- 40x + 60y = 820
To solve the system, we can multiply the first equation by 40 to eliminate x from the second equation:
- 40x + 40y = 600 (after multiplying the first equation by 40)
- 40x + 60y = 820
Subtracting the first modified equation from the second gives us:
Dividing both sides by 20 results in y = 11. This means 11 gallons were used on the highway, which is not one of the options provided. There may have been a mistake in the question or in the options given. Based on the options, the closest correct answer would be 8 gallons used on the highway, which after reevaluating the initial equation, turns out to be the correct answer as seen below:
- x = 15 - y
- 40(15 - y) + 60y = 820
- 600 + 20y = 820
- 20y = 220
- y = 11
With 15 gallons in total and 11 used on the highway, 4 gallons were used in the city (15 - 11 = 4). The initial assumption that x + y = 15 and 40x + 60y = 820 hold true, confirming the usage of 11 gallons on the highway.