Gasoline mixture problem

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} 

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

- Algebra House
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