Question

A car uses 1 gallon of gasoline for every 25 miles driven. At the start of a trip the tank was full of gasoline. After driving 500 miles, there were 2 gallons of gasoline left in the tank.



Which equation shows the amount of gasoline left in the tank, V, as a function of the number of miles driven, d?

Answer options with 5 options
A.
V equals StartFraction d over 25 EndFraction

B.
V equals negative StartFraction d over 25 EndFraction plus 2

C.
V equals StartFraction d over 25 EndFraction plus 22

D.
V equals negative StartFraction d over 25 EndFraction plus 22

E.
V equals StartFraction d over 25 EndFraction plus 2

Answer 1

To determine the correct equation that represents the amount of gasoline left in the tank, \( V \), as a function of the number of miles driven, \( d \), we'll start by analyzing the provided information.

1. The car uses **1 gallon** of gasoline for every **25 miles** driven. Therefore, for **500 miles**, the amount of gasoline used is:

\[
\text{Gasoline used} = \frac{500 \text{ miles}}{25 \text{ miles/gallon}} = 20 \text{ gallons}
\]

2. After driving 500 miles, there are **2 gallons** of gasoline left in the tank. So, at the start of the trip, the tank was full and contained:

\[
\text{Starting gasoline} = \text{gasoline used} + \text{gasoline left} = 20 \text{ gallons} + 2 \text{ gallons} = 22 \text{ gallons}
\]

Now, we establish the relationship between the number of miles driven \( d \) and the amount of gasoline left \( V \). Since the car uses \( \frac{d}{25} \) gallons for \( d \) miles, the gasoline left can be calculated as follows:

\[
V = \text{Starting gasoline} - \text{Gasoline used}
\]

Substituting in the values gives:

\[
V = 22 - \frac{d}{25}
\]

This can be rearranged to:

\[
V = -\frac{d}{25} + 22
\]

Thus, the correct option from the provided choices is:

**D. \( V = -\frac{d}{25} + 22 \)**