Select the correct answer.

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?

A. [tex]y = 256 - 16x[/tex]
B. [tex]y = 448 - 16x[/tex]
C. [tex]y = 448 - 28x[/tex]
D. [tex]y = 16 - 28x[/tex]
E. [tex]y = 256 + 16x[/tex]



Answer :

To solve the problem, let's follow these steps:

1. Determine the total number of miles the car can travel on a full tank:
- The average fuel economy of the car is 28 miles per gallon.
- The capacity of the fuel tank is 16 gallons.
- To find the total number of miles the car can travel with a full tank, simply multiply the fuel economy by the tank capacity:
[tex]\[ \text{Total miles} = 28 \, \text{miles/gallon} \times 16 \, \text{gallons} = 448 \, \text{miles} \][/tex]

2. Formulate the function representing the remaining miles as fuel is consumed:
- Let \( y \) be the remaining miles the car can travel, and \( x \) be the number of gallons consumed.
- If the car starts with 448 miles worth of fuel, the miles left after consuming \( x \) gallons is given by:
[tex]\[ y = 448 - 28x \][/tex]
- Here, \( 28x \) constitutes the miles already traveled (since 28 miles are traveled for each gallon), and subtracting this from the total gives the remaining distance.

3. Identify the correct option:
- The function we derived is:
[tex]\[ y = 448 - 28x \][/tex]
- Comparing this with the provided options, we find that option C matches our derived function:
[tex]\[ \mathbf{C. \ } y=448-28x \][/tex]

Therefore, the correct answer is:
[tex]\[ \boxed{C. \ y = 448 - 28x} \][/tex]

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