Question

Brian decides to mix grades of gasoline in his truck. He puts in7 gallons of regular and5 gallons of premium for a total cost of$45.14. If premium gasoline costs$0.22 more per gallon than regular, what was the price of each grade of gasoline?

Answer 1

In this problem we have two variables, so we need two equation to solve the system.

The first equation comes from the gasoline he puts in his truck so: (R mean the regular gasoline, and P means the premium gasoline)

$7R+5P=45.14$

And the secon equation comes from the value of a individual gallon:

$P=R+0.22$

Now to find the value of the regular gasoline we can replace the second equation into the first equation:

$\begin{gathered} 7R+5(R+0.22)=45.14 \\ 7R+5R+1.1=45.14 \\ 12R=44.04 \\ R=\frac{44.04}{12} \\ R=3.67 \end{gathered}$

Now with the value of R we can rplace that into the second equation:

$\begin{gathered} P=3.67+0.22 \\ P=3.89 \end{gathered}$