Peter decides to mix grades of gasoline in his truck. He puts in 5 gallons of regular and 10 gallons of premium for a total cost of $31.05 If premium gasoline costs $0.18 more per gallon than regular, what was the price of each grade of gasoline?

**x = cost of 5 gallons of regular**

x + 0.18 = cost of 10 gallons of premium{premium is $0.18 more than regular per gallon}

x + 0.18 = cost of 10 gallons of premium

5x + 10(x + 0.18) = 31.05 {number of gallons times price per gallon equals total price}

5x + 10x + 1.8 = 31.05 {used distributive property}

15x + 1.8 = 31.05 {combined like terms}

15x = 29.25 {subtracted 1.8 from each side}

x = 1.95 {divided each side by 15}

x + 0.18 = 2.13 {substituted 1.95, in for x, into x + 0.18}

**$1.95 is the price per gallon of 5 gallons of regular**

$2.13 is the price per gallon of 10 gallons of premium

$2.13 is the price per gallon of 10 gallons of premium

**Ask Algebra House**