Let's solve this step-by-step.
1. First, we know that the total distance for the trip is 200 miles.
2. The Blakely family has already driven 50 miles. To find out how many miles remain, we subtract the miles already driven from the total trip distance:
[tex]\[
\text{Remaining Distance} = \text{Total Trip Distance} - \text{Miles Driven} = 200 \text{ miles} - 50 \text{ miles} = 150 \text{ miles}
\][/tex]
3. Next, we need to determine how many gallons of gasoline are needed to travel the remaining 150 miles. We know that the car travels 30 miles per gallon.
4. To find the number of gallons required, we divide the remaining distance by the car's mileage (miles per gallon):
[tex]\[
\text{Gallons Needed} = \frac{\text{Remaining Distance}}{\text{Miles per Gallon}} = \frac{150 \text{ miles}}{30 \text{ miles per gallon}} = 5 \text{ gallons}
\][/tex]
Therefore, the car will use 5 gallons of gasoline for the remainder of the trip. The correct answer from the options provided is:
5 gallons
