To solve this problem, we need to figure out how many months it would take for the savings on gasoline to cover the additional $5000 cost of the car.

Step 1: Calculate the current annual gasoline consumption.

Your car currently gets 22 miles per gallon, and you drive 10,000 miles per year. So, the amount of gasoline you currently use in a year is:

$\frac{10,000 \text{ miles}}{22 \text{ miles per gallon}} \approx 454.55 \text{ gallons per year}$

Step 2: Calculate the annual gasoline cost with your current car.

Given that the cost of gasoline is $3.00 per gallon, your current annual cost for gasoline is:

$454.55 \text{ gallons} \times 3.00 \text{ dollars per gallon} = 1363.64 \text{ dollars per year}$

Step 3: Calculate the annual gasoline consumption with the new car.

The new car gets 69 miles per gallon. So, the amount of gasoline you would use in a year with the new car is:

$\frac{10,000 \text{ miles}}{69 \text{ miles per gallon}} \approx 144.93 \text{ gallons per year}$

Step 4: Calculate the annual gasoline cost with the new car.

The annual gasoline cost with the new car would be:

$144.93 \text{ gallons} \times 3.00 \text{ dollars per gallon} = 434.79 \text{ dollars per year}$

Step 5: Calculate the annual savings on gasoline.

The savings per year would be the difference between the annual gasoline cost of your current car and the new car:

$1363.64 \text{ dollars} - 434.79 \text{ dollars} = 928.85 \text{ dollars per year}$

Step 6: Calculate how long it will take to save $5000.

Now, divide the additional cost of the car ($5000) by the annual savings:

$\frac{5000 \text{ dollars}}{928.85 \text{ dollars per year}} \approx 5.38 \text{ years}$

Step 7: Convert years into months.

Since there are 12 months in a year, the time in months is:

$5.38 \times 12 \approx 65 \text{ months}$

Conclusion:

It would take approximately 65 months for your savings on gasoline to pay for the increased cost of the car.

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Would you like more details or have any questions?

Here are 5 related questions for further exploration:

1. How would the savings change if the price of gasoline increased to $4.00 per gallon?
2. What if your driving distance increased to 15,000 miles per year?
3. How much would you save on gasoline over a 10-year period with the new car?
4. What if the new car only had an EPA rating of 55 miles per gallon?
5. How does the fuel efficiency of electric vehicles compare in cost savings over gasoline-powered cars?

Tip: Always consider future fluctuations in gasoline prices when calculating long-term savings.