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

A $25,889 regular car whose fuel consumption is 24 miles per gallon.
A $27,184 hybrid car whose fuel consumption is 42 miles per gallon.
If the cost of gas is $2.94 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 find out how many miles you need to drive the hybrid car to recover the cost difference through gas savings, we can follow these steps:

1. **Calculate the cost difference between the two cars:**

   \[
   \text{Cost Difference} = \$27,184 - \$25,889 = \$1,295
   \]

2. **Determine the fuel costs per mile for each car:**

   - For the regular car:  
     \[
     \text{Fuel cost per mile} = \frac{\$2.94}{24 \text{ miles per gallon}} = \$0.1225 \text{ per mile}
     \]
   
   - For the hybrid car:  
     \[
     \text{Fuel cost per mile} = \frac{\$2.94}{42 \text{ miles per gallon}} = \$0.07 \text{ per mile}
     \]

3. **Calculate the savings per mile when driving the hybrid car:**

   \[
   \text{Savings per mile} = \$0.1225 - \$0.07 = \$0.0525 \text{ per mile}
   \]

4. **Find the number of miles needed to cover the cost difference:**

   \[
   \text{Miles to recover cost} = \frac{\text{Cost Difference}}{\text{Savings per mile}} = \frac{\$1,295}{\$0.0525 \text{ per mile}}
   \]

Let's calculate the exact number of miles:

\[
\frac{1295}{0.0525}
\]You would need to drive the hybrid car approximately **24,667 miles** in order for the gas savings to recover the difference in the cost of the two cars.

Would you like to see more details or have any questions about this calculation?

Here are some related questions you might find interesting:

1. How would the answer change if the price of gas increases?
2. What is the break-even point in years if you drive a specific number of miles per year?
3. How does fuel efficiency impact the total cost of ownership over a car's lifetime?
4. What would be the impact of higher or lower gas prices on the break-even mileage?
5. How much would you save annually if you drive a certain number of miles with the hybrid car compared to the regular car?

**Tip:** Consider the maintenance and insurance costs as well, as they can also differ between regular and hybrid cars!

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

A $25,889 regular car whose fuel consumption is 24 miles per gallon.
A $27,184 hybrid car whose fuel consumption is 42 miles per gallon.
If the cost of gas is $2.94 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 many miles you need to drive a hybrid car to recover the cost difference through gas savings. This problem explores concepts like fuel cost per mile and cost efficiency. Step-by-step breakdown included for grades 8-10.

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