Simone rents a compact car that gets 31 miles per gallon. When she rents the car, the price of a gallon of gas is $3.10. The cost C of the gas used to drive the car is a function of the number of miles x that the car is driven.
The cost of renting the car is $0.10 per mile driven.
Write an equation for this function.
Is the problem asking to consider both how many miles driven and how many gallons of gas purchased to find the total cost?
To write the equation for the cost C of gas used to drive the car, we need to consider two factors: the number of miles x that the car is driven, and the gas mileage of the car, which is 31 miles per gallon.
First, we need to find how many gallons of gas are used for x miles driven. Since the car gets 31 miles per gallon, the number of gallons used can be found by dividing the number of miles driven by 31. Therefore, the number of gallons used is x/31.
Next, we can find the cost of the gas used by multiplying the number of gallons used by the price of a gallon of gas, which is $3.10. Therefore, the cost of the gas used is (x/31) * $3.10.
Finally, we need to account for the cost of renting the car, which is $0.10 per mile driven. This cost can be added to the cost of the gas used. Therefore, the final equation for the cost C of the gas used to drive the car is:
C(x) = (x/31) * $3.10 + $0.10x
So, the equation is C(x) = (x/31) * 3.10 + 0.10x.