Question 1121515: want to buy a new car and trying to choose between two models:
• Model A: costs $17,000 and its gas mileage is 20 miles per gallon and its insurance is $200 per year.
• Model B: costs $25,000 and its gas mileage is 35 miles per gallon and its insurance is $400 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 is the independent variable.
• 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 four years, which model is more economical? How about if you plan to keep it for six 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 cost of ownership? Graph or show hand calculations.
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Model A is C=17,000+(40000/20)*3x+200x or 6200x+17000; 5 years, this is $48,000; 4 years: $41,800
Model B is 25000+(40000/35)3x+400x=3828.57x+25000; 5 years, this is $44,142.85; 4 years: $40,314.28
For any year, put that number into x for each.
They are equal when 6200x+17000=3828.57x+25000
2371.43x=8000
x=3.37 years
Double the cost of gas and A will be 17000+12200x and B will be 25000+6857.14x. It would make the Model B a better overall buy much sooner.
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