Kevin 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 $61.30. If premium gasoline costs $0.22 more per gallon than regular, what was the price of each grade of gasoline?
If the regular gas costs x cents/gal, then
5x + 10(x+22) = 6130
Let's assume the price of regular gasoline per gallon is x dollars.
According to the given information, the price of premium gasoline per gallon will be x + 0.22 dollars.
Now, let's calculate the cost of 5 gallons of regular gasoline: 5 * x = 5x dollars.
Similarly, the cost of 10 gallons of premium gasoline can be calculated as: 10 * (x + 0.22) = 10x + 2.2 dollars.
The total cost of the gasoline is $61.30, so we can write the equation: 5x + 10x + 2.2 = 61.30.
Combining like terms, we get: 15x + 2.2 = 61.30.
Subtracting 2.2 from both sides of the equation, we get: 15x = 59.10.
Dividing both sides of the equation by 15, we get: x = 59.10 / 15 = 3.94 dollars.
So, the price of regular gasoline is $3.94 per gallon.
Substituting the value of x in the expression for the price of premium gasoline, we get: x + 0.22 = 3.94 + 0.22 = 4.16 dollars.
Therefore, the price of premium gasoline is $4.16 per gallon.
To solve this problem, we can set up a system of equations.
Let's assume the price of regular gasoline is "x" dollars per gallon.
Since premium gasoline costs $0.22 more per gallon than regular, the price of premium gasoline would be "x + 0.22" dollars per gallon.
Now, let's set up the equations based on the information given:
Equation 1: Cost of regular gasoline + Cost of premium gasoline = Total cost
5x + 10(x + 0.22) = 61.30
Now, let's solve the equation step by step:
Step 1: Distribute the 10 to (x + 0.22):
5x + 10x + 2.20 = 61.30
Step 2: Combine like terms:
15x + 2.20 = 61.30
Step 3: Subtract 2.20 from both sides of the equation:
15x = 59.10
Step 4: Divide both sides by 15:
x = 3.94
So, the price of regular gasoline is $3.94 per gallon.
Now, let's find the price of premium gasoline:
x + 0.22 = 3.94 + 0.22 = 4.16
Therefore, the price of premium gasoline is $4.16 per gallon.