Question

Sully’s car has an average fuel economy of 28 miles per gallon. The capacity of the fuel tank is 16 gallons. If Sully completely fills the tank, which function represents the number of miles the car can go without refueling in terms of the gallons of fuel it consumes? (Hint: Convert the car’s fuel tank capacity in gallons to the number of miles the car can travel.) A. y = 256 − 16x B. y = 448 − 16x C. y = 448 − 28x D. y = 16 − 28x E. y = 256 + 16x

Answer 1

The correct function that represents the number of miles Sully's car can travel without refueling in terms of the gallons of fuel it consumes is y = 448 - 28x, which corresponds to option C.

Step-by-step explanation:

The student is asking for a function that represents the number of miles Sully's car can travel without refueling based on the gallons of fuel consumed. Given that the car has an average fuel economy of 28 miles per gallon and the capacity of the fuel tank is 16 gallons, we can create an equation.

First, calculate the maximum distance the car can travel on a full tank by multiplying the fuel economy by the tank capacity:

• Maximum distance = 28 miles/gallon × 16 gallons = 448 miles

Therefore, the car can travel up to 448 miles on a full tank. To represent the remaining distance as a function of the gallons consumed (x), we subtract the product of the number of gallons used and the fuel economy (28 miles/gallon) from the maximum distance:

• Remaining distance (y) = 448 miles - (28 miles/gallon × x gallons)

The correct function is therefore:

• y = 448 - 28x

This corresponds to option C: y = 448 - 28x.