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.
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The car uses 1 gallon of gasoline for every 25 miles driven. Therefore, for 500 miles, the amount of gasoline used is:
\[ \text{Gasoline used} = \frac{500 \text{ miles}}{25 \text{ miles/gallon}} = 20 \text{ gallons} \]
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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. \( V = -\frac{d}{25} + 22 \)
1 answer