Suppose you are shopping for a new car, and you've narrowed your search to two options:

A $25,107 regular car whose fuel consumption is 23 miles per gallon.
A $27,543 hybrid car whose fuel consumption is 42 miles per gallon.
If the cost of gas is $2.53 per gallon, how many miles would you have to drive the hybrid car in order for the gas savings to recover the difference in the cost of the two cars?

Round your answer to the nearest mile (whole number). 

To determine how many miles you would need to drive the hybrid car to recover the cost difference, we can follow these steps:

### Step 1: Define Variables
- **Cost of the regular car** = \$25,107
- **Cost of the hybrid car** = \$27,543
- **Fuel consumption of regular car** = 23 miles per gallon (MPG)
- **Fuel consumption of hybrid car** = 42 miles per gallon (MPG)
- **Cost of gas** = \$2.53 per gallon

### Step 2: Calculate the Cost Difference
The price difference between the regular car and the hybrid car is:
\[
\text{Cost Difference} = 27,543 - 25,107 = 2,436
\]
So, you need to recover \$2,436 through fuel savings.

### Step 3: Determine Fuel Costs per Mile
- **Fuel cost per mile for the regular car**:
\[
\text{Cost per mile (regular)} = \frac{2.53}{23} \approx 0.1100 \text{ dollars per mile}
\]
- **Fuel cost per mile for the hybrid car**:
\[
\text{Cost per mile (hybrid)} = \frac{2.53}{42} \approx 0.0602 \text{ dollars per mile}
\]

### Step 4: Calculate Fuel Savings per Mile
The fuel savings per mile when driving the hybrid car is the difference between the regular and hybrid cars' fuel costs:
\[
\text{Savings per mile} = 0.1100 - 0.0602 = 0.0498 \text{ dollars per mile}
\]

### Step 5: Determine the Break-Even Mileage
To recover the \$2,436 price difference through fuel savings, you need to drive:
\[
\text{Miles to break even} = \frac{2,436}{0.0498} \approx 48,915 \text{ miles}
\]

Thus, you would need to drive approximately **48,915 miles** to recover the cost difference between the two cars.

Would you like further details or have any questions?

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Here are 5 questions to deepen your understanding:
1. How would changes in gas prices affect the break-even mileage?
2. What if the fuel consumption of the regular car were slightly better—how would that change the calculations?
3. How does the cost of gas influence the decision to buy a hybrid car?
4. What are the long-term savings if you drive more than the break-even mileage?
5. How could maintenance costs affect your decision between the two cars?

**Tip:** When evaluating long-term costs, remember to also factor in maintenance and insurance costs, as hybrids may have different expenses in these areas compared to regular cars.

Suppose you are shopping for a new car, and you've narrowed your search to two options: A $25,107 regular car whose fuel consumption is 23 miles per gallon. A $27,543 hybrid car whose fuel consumption is 42 miles per gallon. If the cost of gas is $2.53 per gallon, how many miles would you have to drive the hybrid car in order for the gas savings to recover the difference in the cost of the two cars? Round your answer to the nearest mile (whole number).

Find out how to calculate the number of miles you need to drive a hybrid car to recover the cost difference with a regular car. This problem includes detailed cost-benefit analysis, fuel consumption rates, and fuel savings per mile calculations. Suitable for Grades 10-12 students.

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