Question

Anna has decided to purchase a small car with a small gas tank. If x represents the number of miles driven, which linear function would best ESTIMATE the gas in Anna's tank as she drives?

A) y = 20 - 0.05x
B) y = 25 - 0.05x
C) y = 12 + 0.05x
D) y = 10 - 0.05x

Answer 1

D) y = 10 - 0.05x

Explanation:

The number of gallons of gas left in the tank of Anna's car can be represented using a linear function in the form

`y=q+mx`

where

x is the number of miles driven

q is the amount of gallons initially in the tank, when x = 0

m is the number of gallons consumed per mile driven

First of all, we observe that:

- The sign of m must be negative, because as the car drives, the number of gallons left in the tank (y) must decrease. Therefore, we can immediately exclude option C)

- The problem says that the car has a small tank. Therefore, the number of gallons in the tank at the beginning must be the minimum possible, so in this case, q = 10

Therefore, the correct function is:

y = 10 - 0.05x

which means that: at the beginning, the tank contains 10 gallons, and 0.05 gallons per mile are consumed as the car moves.