E-Z Stop Fast Gas sold $10,957 worth of gasoline yesterday. Regular sold for $2.30 a gallon, and premium sold for $2.55 a gallon. If the station sold 420 more gallons of regular than of premium:
a. How many gallons of each type of gasoline were sold?
Do not enter units in your answer.
Premium: ___________ gallons
Regular: ___________ gallons
b. If the profit on regular gas is $0.18 per gallon and on premium is $0.20 per gallon, what was the station's total profit?
$___________
a. X Gal. of premium.
(x+420) Gal. of regular
2.55x + 2.30(x+420) = $10,957
Solve for X.
To solve this problem, we can use a system of equations. Let's define the variables:
Let R represent the number of gallons of regular gasoline sold.
Let P represent the number of gallons of premium gasoline sold.
We are given the following information:
R + P = (Total gallons sold)
R = P + 420 (Regular gallons sold 420 more than premium gallons)
2.30R + 2.55P = 10,957 (Total sales revenue)
Now, we can solve this system of equations.
First, we can substitute the value of R in terms of P from the second equation into the first equation:
(P + 420) + P = (Total gallons sold)
2P + 420 = (Total gallons sold)
Next, we can substitute the value of R in terms of P from the second equation into the third equation:
2.30(P + 420) + 2.55P = 10,957
Now, we can solve these equations to find the values of P and R.
a. Solving the system of equations:
2P + 420 = (Total gallons sold) - P
3P = (Total gallons sold) - 420
P = [(Total gallons sold) - 420] / 3
Substituting the value of P into the second equation:
2.30([(Total gallons sold) - 420] / 3 + 420) + 2.55P = 10,957
Simplifying the equation:
(2.30 / 3)(Total gallons sold) + (2.30 * 420 / 3) + 2.55P = 10,957
(2.30 / 3)(Total gallons sold) + 322 + 2.55P = 10,957
Now, we can solve for P:
2.85P = 10,957 – (2.30 / 3)(Total gallons sold) - 322
P = [10,957 – (2.30 / 3)(Total gallons sold) - 322] / 2.85
We can substitute this value of P back into the equation R = P + 420 to find R.
b. The total profit can be calculated by multiplying the number of gallons sold by the profit per gallon and then adding them:
Total Profit = (Profit per gallon of regular * R) + (Profit per gallon of premium * P)
Substituting the values obtained for R and P into the equation:
Total Profit = (0.18 * R) + (0.20 * P)
Now, you can plug in the values for (Total gallons sold) to find P and R, and then calculate the total profit.