Question

Nelson decides to mix grades of gasoline in his truck. He puts in 9 gallons of regular and 7 gallons of premium for a total cost of $27.71. If premium gasoline costs $0.21 more per gallon than regular, what was the price of each grade of gasoline?

Answer 1

The prices of the two grades of gasoline were found using a system of equations. Regular gasoline was $1.64 per gallon and premium was $1.85 per gallon, with the premium costing $0.21 more per gallon than the regular.

Step-by-step explanation:

Nelson is mixing two grades of gasoline, regular and premium, for his truck. He purchases 9 gallons of regular and 7 gallons of premium, spending a total of $27.71. The premium gasoline costs $0.21 more per gallon than the regular. To find the price per gallon of each type of gasoline, we will set up a system of equations and solve for the two unknowns: the cost of regular gasoline per gallon (R) and the cost of premium gasoline per gallon (P).

Firstly, we know from the problem that:

1. P = R + 0.21
2. 9R + 7P = 27.71

Substituting the first equation into the second, we get:

9R + 7(R + 0.21) = 27.71

9R + 7R + 1.47 = 27.71

We now combine like terms:

16R + 1.47 = 27.71

Subtract 1.47 from both sides to isolate the variable R:

16R = 26.24

Divide by 16 to solve for R:

R = 1.64

Now we know the cost of regular gasoline is $1.64 per gallon, we can find the cost of premium by adding $0.21:

P = 1.64 + 0.21

P = 1.85

Therefore, the price of regular gasoline was $1.64 per gallon and the price of premium gasoline was $1.85 per gallon.