Final answer:
To represent the cost of premium gasoline in terms of regular gasoline, we add $0.20 to the cost of regular gasoline, denoted as r. The equation for the total cost of 10 gallons of regular and 15 gallons of premium gasoline, which amounts to $32.75, is expressed as (r × 10) + ((r + $0.20) × 15) = $32.75.
Step-by-step explanation:
To write an equation representing the cost of premium gasoline in terms of regular gasoline, we first need to express this relationship mathematically. If we denote the cost per gallon of regular gasoline as r, then the cost per gallon of premium gasoline would be r + $0.20, since it is given that premium gas costs $0.20 more per gallon than regular gas.
Now, let's write an equation for the total cost of the gasoline. Using the variables described, the equation for the total cost would be:
Total cost = (cost per gallon of regular gas × number of gallons of regular gas) + (cost per gallon of premium gas × number of gallons of premium gas)
Therefore, the equation is:
Total cost = (r × 10) + ((r + $0.20) × 15) = $32.75
To answer the student's question, you would solve for r which is the cost of regular gasoline per gallon and then add $0.20 to it to find the cost per gallon of premium gasoline.