**Learning Goal: **I’m working on a algebra multi-part question and need the explanation and answer to help me learn.

Suppose you want to buy a new car and are trying to choose between two models:

- Model A: costs $16,500 and its gas mileage is 25 miles per gallon and its insurance is $250 per year.
- Model B: costs $24,500 and its gas mileage is 40 miles per gallon and its insurance is $450 per year.

If you drive approximately 40,000 miles per year and the gas costs $3 per gallon:

- Find a formula for the total cost of owning Model A where the number of years you own the car is represented by x.
- Find a formula for the total cost of owning Model B where the number of years is the independent variable.
- Find the total cost for each model for the first five years.
- If you plan to keep the car for 4 years, which model is more economical? What about if you plan to keep it for 6 years?
- Find the number of years in which the total cost to keep the two cars will be the same.
- Identify the number of months where neither car holds a cost of ownership advantage.
- What effect would the cost of gas doubling have on the cost of ownership? Graph or show hand calculations.
- If you can sell either car for 40% of its value at any time, how does the analysis change? Graph or show hand calculations.

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