Final answer:
After setting up and solving a system of equations, we find that Pitt's Pit Stop sold 2,510 gallons of regular gasoline and 2,150 gallons of premium gasoline, earning a total profit of $763.50.
Step-by-step explanation:
To solve this problem, we can use a system of equations because we have two unknowns (the number of gallons of regular and premium gasoline sold) and two pieces of information that can be turned into equations.
Step 1: Define the variables
Let x be the number of gallons of premium gasoline sold and x + 360 be the number of gallons of regular gasoline sold, as the station sold 360 more gallons of regular than premium.
Step 2: Set up the equations
The first equation comes from the total sales value:
3.30(x + 360) + 3.45x = 15,700.50
The second equation is implied by the fact there are 360 more gallons of regular sold than premium:
Regular (x + 360) – Premium (x) = 360
Step 3: Solve the system of equations
Using the first equation, we can solve for x:
3.30x + 1,188 + 3.45x = 15,700.50
6.75x + 1,188 = 15,700.50
6.75x = 14,512.50
x = 2,150
So, the number of gallons of premium sold is 2,150 and the number of gallons of regular sold is 2,150 + 360 = 2,510.
Step 4: Calculate the total profit
The profit for regular gas per gallon is $0.15 and for premium gas is $0.18. The total profit is then calculated by:
Profit from Regular = $0.15 × 2,510
Profit from Premium = $0.18 × 2,150
Total Profit = (0.15 × 2,510) + (0.18 × 2,150)
After performing the calculations, we find:
Profit from Regular = $376.50
Profit from Premium = $387
Total Profit = $376.50 + $387 = $763.50
Therefore, the total profit was $763.50.