Question

Peter decides to mix grades of gasoline in his truck. He puts in 6 gallons of regular and 7 gallons of premium for a total cost of $34.09. If premium gasoline costs $0.19 more per gallon than regular, what was the price of each grade of gasoline?

Answer 1

ANSWER

The price of the gallons of regular is $2.52

The price of the gallons of premium is $1.52

Explanation

Given information

The total cost of 6 gallons of regular and the7 gallons of premium = $34.09

The gallons of premium gasoline cost $0.19 more per gallon than gallons of regular.

Let x represents the gallons of premium gasoline

Let y represents the gallons of regular

The next step is to set up the system of linear equations.

For the first information, we have 7 gallons of premium and 6 gallons of regular gasoline

`7x\text{ + 6y = 34.09 ----- equation 1}`

Recall, gallons of premium is $0.19 more per gallon in regular

Mathematically

`x\text{ = 0.19 + y -------- equation }2`

The next step is to solve the equation simultaneously using the substitution method'

Substitute the value of x in equation 2 into equation 1

`\begin{gathered} 7(0.19\text{ + y) + 6y = 34.09} \\ 1.33\text{ + 7y + 6y = 34.09} \\ 1.33\text{ + 13 y = 34.09} \\ \text{subtract 1.33 from both sides} \\ 1.33\text{ - 1.33 + 13y = 34.09 - 1.33} \\ 13y\text{ = }32.76 \\ \text{Divide both sides by13} \\ (13y)/(13)\text{ = }(32.76)/(13) \\ y\text{ = \$2.52} \end{gathered}`

Hence, the price of the gallons of regular is $2.52

The next step is to find the value of x

`\begin{gathered} \text{Recall, x = 019 + y} \\ x\text{ = 0.19 + 1.33} \\ x\text{ = \$1.52} \end{gathered}`

Hence, the price of the gallons of premium is $1.52