Final answer:
The total cost of buying a car wash and x gallons of gasoline is represented by the equation y = 5 + 3.10x, which includes a fixed cost of $5 for the car wash and $3.10 per gallon of gasoline.
Step-by-step explanation:
The equation that represents y, the total cost of buying a car wash and x gallons of gasoline at the gas station is y = 5 + 3.10x.
In this equation, the constant value 5 represents the fixed cost of the car wash. The variable x stands for the number of gallons of gasoline purchased, and the number 3.10 is the cost per gallon of gasoline. When you multiply 3.10 by x (the number of gallons), you get the total cost for the gasoline. By adding the fixed car wash cost to the total gasoline cost, you arrive at the total cost y.
For example, if a customer buys 10 gallons of gasoline, the total cost would be calculated as follows: y = 5 + 3.10(10), which simplifies to y = 5 + 31, so y = 36 dollars.