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Let's analyze the situation by calculating the miles per gallon (mpg) for both David and Dennis.

1. **David's car:**
   - Miles driven: 384 miles
   - Gallons used: 12 gallons
   - MPG: \( \frac{384 \text{ miles}}{12 \text{ gallons}} = 32 \text{ mpg} \)

2. **Dennis's car:**
   - Miles driven: 324 miles
   - Gallons used: 9 gallons
   - MPG: \( \frac{324 \text{ miles}}{9 \text{ gallons}} = 36 \text{ mpg} \)

Now, let's evaluate the statements:

- **Statement A: "David’s car has an mpg greater than Dennis’ car’s mpg."**
  - This is **false** because David's car has 32 mpg, which is less than Dennis’s 36 mpg.

- **Statement B: "David’s and Dennis’ cars have the same mpg."**
  - This is **false** because their mpg values are different (32 vs. 36).

- **Statement C: "The difference between the two cars’ mpg is 4."**
  - This is **true** because the difference is \( 36 - 32 = 4 \).

- **Statement D: "Dennis’ car has an mpg of 36."**
  - This is **true** because we calculated Dennis’s mpg as 36.

- **Statement E: "Dennis’ car will use 5 gallons of gas if driving 160 miles."**
  - To check this, we use the formula: \( \text{Gallons used} = \frac{\text{Miles driven}}{\text{MPG}} \).
  - For Dennis: \( \frac{160 \text{ miles}}{36 \text{ mpg}} \approx 4.44 \text{ gallons} \).
  - This is **false** because the exact amount of gas used is about 4.44 gallons, not 5 gallons.

**Correct Answers:**
- **C** and **D** are the correct statements.

Would you like any further details or explanations?

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**Relative Questions:**

1. How would the mpg change if David used more gallons of gas for the same distance?
2. If Dennis drove an additional 100 miles using 2.5 more gallons of gas, what would his new mpg be?
3. How would the cost of fuel affect the comparison if David and Dennis paid different prices per gallon?
4. How would the comparison change if David's car improved its fuel efficiency by 10%?
5. What if Dennis's car had a malfunction causing it to use 20% more fuel per mile—how would this affect his mpg?

**Tip:** When calculating miles per gallon (mpg), ensure that the units are consistent and that the total miles are divided by the total gallons used for accuracy.

Two brothers each buy a new car. In the first week after buying the cars, David drives his car 384 miles and uses 12 gallons of gas. Dennis drives his car 324 miles and uses 9 gallons of gas. Select TWO statements that are true about the situation.
A. David’s car has an mpg (miles per gallon) greater than Dennis’ car’s mpg.
B. David’s and Dennis’ cars have the same mpg.
C. The difference between the two cars’ mpg is 4.
D. Dennis’ car has an mpg of 36.
E. Dennis’ car will use 5 gallons of gas if drive 160 miles.

Determine the miles per gallon (MPG) for two brothers' cars based on their driving data. Learn how to compare fuel efficiency using simple arithmetic calculations. Suitable for students in Grades 5-7.

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