Algebra

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

  1. Model A: costs $16,500 and its gas mileage is 25 miles per gallon and its insurance is $250 per year.
  2. 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:

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