To find the equation that represents the number of gallons of gas, \( y \), in Margo's car after driving \( x \) miles, we need to consider the following:
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Gas consumption rate: Margo's car uses \( \frac{1}{50} \) gallon of gas per mile. Therefore, if she drives \( x \) miles, the amount of gas consumed will be \( \frac{x}{50} \) gallons.
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Initial amount of gas: Margo starts with a full tank. We need to determine how much gas was in the tank initially. Since she drove 200 miles and had 8 gallons left at her destination, we can calculate how much gas was in the tank before the drive.
- Calculate gas consumed for 200 miles: \[ \text{Gas consumed} = \frac{200}{50} = 4 \text{ gallons} \]
- If there are 8 gallons left after the trip, then the total gas at the start (initially in the tank) must be: \[ \text{Initial amount} = 8 \text{ gallons (remaining)} + 4 \text{ gallons (consumed)} = 12 \text{ gallons} \]
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Constructing the equation: After driving \( x \) miles, the number of gallons remaining in the tank would be: \[ y = \text{Initial amount} - \text{Gas consumed} = 12 - \frac{x}{50} \] This can be rewritten as: \[ y = -\frac{1}{50} x + 12 \]
Based on the options given, the equation that matches our derived equation is:
B. \( y = -\frac{1}{50} x + 12 \).
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