Final answer:
By setting up equations based on the amounts of gas bought and the prices paid, we can determine the prices per gallon of mid-grade and regular gas. None of the provided options match the total costs exactly, indicating there may be a typo or error in the options.
Step-by-step explanation:
To solve for the prices per gallon of mid-grade and regular gas, we can set up a system of equations using the information provided about the amounts of gas purchased and the total cost. Let's denote the price per gallon of mid-grade gas as m and the price per gallon of regular gas as r.
From the first visit, we know that Tom bought 18 gallons of mid-grade gas and 5 gallons of regular gas for a total of $59.91. This can be represented as the equation 18m + 5r = 59.91.
In the second visit, Tom bought 14 gallons of mid-grade gas and 1 gallon of regular gas, paying $39.75, leading us to another equation 14m + r = 39.75.
To find the values for m and r, we can solve this system of equations. However, based on the options provided, we can check which one satisfies both equations:
- A. If we assume mid-grade is $2.49 and regular is $2.99, the first visit would cost 18 * 2.49 + 5 * 2.99 = 44.82 + 14.95 = 59.77, not 59.91.
- B. If we assume mid-grade is $2.79 and regular is $3.09, the first visit would cost 18 * 2.79 + 5 * 3.09 = 50.22 + 15.45 = 65.67, which is not correct.
- C. If we assume mid-grade is $2.99 and regular is $2.49, the first visit would cost 18 * 2.99 + 5 * 2.49 = 53.82 + 12.45 = 66.27, which is not correct.
- D. If we assume mid-grade is $3.09 and regular is $2.79, the first visit would cost 18 * 3.09 + 5 * 2.79 = 55.62 + 13.95 = 69.57, which is not correct.
Since none of the options exactly match the total cost of $59.91, there must be a typo or error within the options provided.