Suppose that two certain cars have the following average operating and ownership costs.
| | Average Costs per Mile |
| :----- | :------------------------------------------------ |
| | Operating | Ownership | Total |
| Car A | $0.26 | $0.68 | $0.94 |
| Car B | $0.17 | $0.28 | $0.45 |
If you drive 20,000 miles per year, by how much does the total annual expense for Car A exceed that of Car B over six years?
The total annual expense for Car A exceeds that of Car B by $$\square$$
(Round to the nearest dollar as needed.)
Answer (1)
Calculate the annual expense for Car A: 0.94 × 20000 = 18800 .
Calculate the annual expense for Car B: 0.45 × 20000 = 9000 .
Find the difference in annual expenses: 18800 − 9000 = 9800 .
Calculate the total difference over six years: 9800 × 6 = 58800 . The total annual expense for Car A exceeds that of Car B by 58800 .
Explanation
Problem Analysis We are given the average operating and ownership costs per mile for two cars, Car A and Car B. We need to find by how much the total annual expense for Car A exceeds that of Car B over six years, assuming a constant 20,000 miles driven per year.
Annual Expense for Car A First, we calculate the total annual expense for Car A. The total cost per mile for Car A is $0.94, and we drive 20,000 miles per year. So, the annual expense for Car A is: 0.94 × 20000 = 18800
Annual Expense for Car B Next, we calculate the total annual expense for Car B. The total cost per mile for Car B is $0.45, and we drive 20,000 miles per year. So, the annual expense for Car B is: 0.45 × 20000 = 9000
Difference in Annual Expenses Now, we find the difference in annual expenses between Car A and Car B: 18800 − 9000 = 9800
Total Difference Over Six Years We need to find the total difference in expenses over six years. So, we multiply the difference in annual expenses by 6: 9800 × 6 = 58800
Final Answer Therefore, the total annual expense for Car A exceeds that of Car B by $58,800 over six years.
Examples
Understanding the long-term costs of owning a car can greatly influence your financial decisions. For instance, if you're deciding between two job offers, one closer to home and one further away, calculating the difference in commuting costs using the method above can help you make a more informed decision. By comparing the total expenses over several years, including fuel, maintenance, and other operating costs, you can accurately assess the financial impact of each job's location. This approach ensures that you're not just considering the salary but also the associated costs, leading to better financial planning and decision-making.
