To determine the equation that represents the number of gallons of gas \( y \) in Margo’s car after she drives \( x \) miles, we first need to calculate how much gas is used during the trip.
Margo's car consumes \( \frac{1}{50} \) gallon of gas per mile. Therefore, for \( x \) miles driven, the amount of gas used is given by:
\[ \text{Gas used} = \frac{1}{50} \cdot x \]
If the car's gas tank was full when Margo left and we denote the total capacity of the tank as \( C \) gallons (initially unknown), the amount of gas remaining in the tank after driving \( x \) miles can be expressed as:
\[ y = C - \frac{1}{50} \cdot x \]
According to the information provided, when Margo arrived at her aunt's house after driving 200 miles, the tank contained 8 gallons of gas. Therefore, we can substitute \( x = 200 \) and \( y = 8 \) into the equation to find \( C \):
\[ 8 = C - \frac{1}{50} \cdot 200 \]
Calculating the gas used for 200 miles:
\[ \frac{1}{50} \cdot 200 = 4 \text{ gallons} \]
Substituting that value back into the equation:
\[ 8 = C - 4 \]
Solving for \( C \):
\[ C = 8 + 4 = 12 \text{ gallons} \]
Now that we have determined the total capacity of the tank is 12 gallons, we can write the equation for the number of gallons of gas \( y \) remaining in the car's tank after driving \( x \) miles:
\[ y = 12 - \frac{1}{50} \cdot x \]
Thus, the final equation representing the number of gallons of gas in the car's tank after Margo drives the car \( x \) miles is:
\[ y = 12 - \frac{1}{50}x \]