Final answer:
To find the price per gallon for regular and premium gasoline, we created a system of equations. Solving the equations reveals that the price per gallon for regular gasoline is approximately $1.72 and for premium gasoline, it's approximately $2.22.
Step-by-step explanation:
The question involves determining the price per gallon for regular and premium gasoline given the total cost and the price difference between the two. Let's denote the price per gallon of regular gasoline as R and the price per gallon of premium gasoline as P. According to the information provided, we know that premium gasoline costs fifty cents ($0.50) more than regular gasoline, so P = R + $0.50.
We have two types of gasoline, 15 gallons of regular and 12 gallons of premium, totaling $52.44. The equation representing this information would be: 15R + 12P = $52.44. Since premium is fifty cents more than regular, we have another equation: P = R + $0.50. Now we can substitute for P in the first equation: 15R + 12(R + $0.50) = $52.44.
Simplifying the equation gives us: 15R + 12R + $6 = $52.44, which combines to 27R + $6 = $52.44. Solving for R, we subtract $6 from both sides, yielding 27R = $46.44. To find R, divide both sides by 27: R = $46.44 / 27, R ≈ $1.72 per gallon for regular. To find P, simply add $0.50 to R: P ≈ $1.72 + $0.50, P ≈ $2.22 per gallon for premium.