To solve this problem, we'll break it down into manageable steps. We'll identify the remaining miles they need to drive and then determine how many gallons of gasoline they will need for the remainder of the trip.
### Step-by-Step Solution:
1. Total Trip Distance: The total distance of the trip is 200 miles.
2. Miles Already Driven: The Blakely family has already driven 50 miles.
3. Miles Remaining:
- To find out how many miles are left, subtract the miles already driven from the total trip distance:
[tex]\[
\text{Remaining miles} = \text{Total trip miles} - \text{Miles driven}
\][/tex]
[tex]\[
\text{Remaining miles} = 200 \text{ miles} - 50 \text{ miles} = 150 \text{ miles}
\][/tex]
4. Car's Fuel Efficiency: The car travels 30 miles per gallon of gas.
5. Gallons Needed for Remaining Miles:
- To find out how many gallons of gas are needed for the remaining 150 miles, divide the remaining miles by the car's fuel efficiency:
[tex]\[
\text{Gallons needed} = \frac{\text{Remaining miles}}{\text{Miles per gallon}}
\][/tex]
[tex]\[
\text{Gallons needed} = \frac{150 \text{ miles}}{30 \text{ miles per gallon}} = 5 \text{ gallons}
\][/tex]
### Final Answer:
The car will use [tex]\(\boxed{5}\)[/tex] gallons of gasoline on the remainder of the trip.
Choosing from the options given:
- [tex]\(2 \frac{1}{2}\)[/tex] gallons
- 4 gallons
- 5 gallons
- [tex]\(8 \frac{1}{3}\)[/tex] gallons
The correct answer is 5 gallons.
