To solve this problem, we need to determine how many gallons of gas Clara should expect to use on a 250-mile road trip, given her car's gas consumption on a 160-mile trip.

Step 1: Calculate the fuel efficiency (miles per gallon)

Clara's car used 7 ¾ gallons of gas for a 160-mile trip. First, let's convert 7 ¾ into an improper fraction or a decimal:

$7 \frac{3}{4} = 7 + \frac{3}{4} = \frac{28}{4} + \frac{3}{4} = \frac{31}{4} = 7.75 \, \text{gallons}$

Now, we find the miles per gallon (MPG) by dividing the distance by the amount of gas used:

$\text{MPG} = \frac{160 \, \text{miles}}{7.75 \, \text{gallons}} = 20.65 \, \text{miles per gallon}$

Step 2: Calculate the amount of gas for a 250-mile trip

Now that we know the car gets 20.65 miles per gallon, we can calculate how many gallons would be needed for a 250-mile trip by dividing 250 miles by the MPG:

$\text{Gallons needed} = \frac{250 \, \text{miles}}{20.65 \, \text{miles per gallon}} \approx 12.11 \, \text{gallons}$

So, Clara should expect to use approximately 12.11 gallons of gas on the 250-mile trip.

Would you like more details or have any other questions?

Here are 5 related questions to extend the topic:

1. How would the fuel consumption change if the trip were 300 miles instead of 250 miles?
2. If Clara used 9 gallons of gas on a 180-mile trip, what would the fuel efficiency be?
3. How could the fuel consumption be reduced through driving habits?
4. What is the significance of calculating MPG in real-life driving scenarios?
5. How do changes in terrain or driving speed affect fuel efficiency?

Tip: Always check for opportunities to maintain steady speeds while driving, as rapid acceleration and braking can reduce fuel efficiency!