Ben wants to buy a new car, and she has narrowed her choices to two models.
Model A sells for $12,500, gets 25mi/gal, and costs $300 a year for insurance
Model B sells for $16,100, gets 36 mi/gal, and costs $400 a year for insurance.
Jenny drives about 36,000 miles a year, and gas costs about $3 a gallon.
a. Find a formula for the total cost of owing Model A for any number of years.
b. Find a formula for the total cost of owing Model B for any number of years.
c. Make a table of the total cost of owning each model from 1 year to 6 years, in 1 year increments.
d. If Ben expects to keep the car for 2 years, which model is more economical?
e. What do you suppose is causing this trend?
I need help with questions a-e please. I am having a difficult starting the problems.
Sure! Let's break down each question and work through them step by step.
a. Find a formula for the total cost of owning Model A for any number of years:
To find the total cost of owning Model A, we need to consider the initial cost of the car, the cost of gas, and the cost of insurance. Since Jenny drives 36,000 miles a year and the car gets 25 miles per gallon, she would need 36,000 miles / 25 miles per gallon = 1,440 gallons of gas per year. Thus, the cost of gas per year would be 1,440 gallons * $3 per gallon = $4,320 per year. The total cost of owning Model A for any number of years can be calculated using the formula:
Total Cost of Model A = Initial cost of Model A + (Cost of gas per year * Number of years) + (Cost of insurance per year * Number of years)
b. Find a formula for the total cost of owning Model B for any number of years:
Using a similar approach, we can find the cost of owning Model B. The cost of gas per year for Model B would be 36,000 miles / 36 miles per gallon = 1,000 gallons of gas per year. Thus, the cost of gas per year would be 1,000 gallons * $3 per gallon = $3,000 per year. The total cost of owning Model B for any number of years can be calculated using the formula:
Total Cost of Model B = Initial cost of Model B + (Cost of gas per year * Number of years) + (Cost of insurance per year * Number of years)
c. To create a table of the total cost of owning each model from 1 year to 6 years, in 1-year increments, you can substitute the number of years (1 to 6) into the formulas we obtained in parts (a) and (b) and calculate the total cost for each year. The table will have two columns, one for the total cost of Model A and another for the total cost of Model B.
d. To determine which model is more economical if Ben expects to keep the car for 2 years, calculate the total cost of owning each model for 2 years using the formulas from parts (a) and (b). Compare the two values and choose the model with the lower total cost.
e. From the given information, we can observe that Model B has a higher initial cost, higher insurance cost, but better mileage compared to Model A. This means that although Model B costs more upfront, it can potentially save money in the long run due to better fuel efficiency. The higher mileage per gallon reduces the amount spent on gas each year, offsetting the higher insurance cost.
I hope this helps clarify the steps involved in answering these questions! Let me know if you have any further questions.