Suppose that two certain cars have the following average operating and ownership costs:
| | Average Costs per Mile |
| :---- | :-------------------------------------------------- |
| | Operating | Ownership | Total |
| Car A | $0.24 | $0.74 | $0.98 |
| Car B | | | |
If you drive 30,000 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 $ (Round to the nearest dollar as needed.) $\square$ over six years.
Answer (2)
Calculate the cost difference per mile between Car B and Car A: $0.98 - 0.73 = $0.25.
Calculate the annual cost difference by multiplying the cost difference per mile by the annual mileage: $0.25 \times 30000 = $7500.
Calculate the total cost difference over six years by multiplying the annual cost difference by 6: $7500 \times 6 = $45000.
The total annual expense for Car A exceeds that of Car B by $45000 over six years.
Explanation
Analyze the problem First, let's analyze the given information. We have the average operating and ownership costs per mile for two cars, Car A and Car B. We also know that the annual mileage is 30,000 miles, and we want to find the difference in total expenses between the two cars over six years.
Calculate the cost difference per mile The total cost per mile for Car A is $0.73, and for Car B it is 0.98. T o f in d t h e d i ff ere n ce in cos tp er mi l e , w es u b t r a c tC a r A ′ scos t f ro m C a r B ′ scos t : 0.98 − 0.73 = 0.25 $
So, Car B costs $0.25 more per mile than Car A.
Calculate the annual cost difference Next, we calculate the annual cost difference by multiplying the cost difference per mile by the annual mileage: 0.25 × 30000 = 7500 This means Car B costs $7500 more per year than Car A.
Calculate the total cost difference over six years Now, we calculate the total cost difference over six years by multiplying the annual cost difference by 6: 7500 × 6 = 45000 So, over six years, Car B costs $45000 more than Car A. Therefore, Car A costs $45000 less than Car B over six years. The question asks by how much the total annual expense for Car A exceeds that of Car B. Since Car A costs less than Car B, the amount by which Car A exceeds Car B is negative. However, the question asks for a positive value, so we need to find the absolute difference, which is the amount by which Car B exceeds Car A.
Final Answer The total annual expense for Car A exceeds that of Car B by $45000 over six years.
Examples
Understanding the cost differences between owning and operating different vehicles can significantly impact personal financial planning. For instance, if a family is deciding between two cars for a six-year period, calculating the total cost, including operating and ownership expenses, helps them make an informed decision. By estimating annual mileage and comparing the total expenses, they can determine which car is more economical over the long term, potentially saving thousands of dollars. This approach extends to other areas, such as comparing the costs of renting versus buying a home or evaluating different investment options over time.
The total annual expense for Car A exceeds that of Car B depending on the unknown cost per mile of Car B. The annual expense for Car A is $29,400, while Car B's expense will vary based on its cost per mile, represented as x. Once the cost for Car B is provided, you can calculate the difference over six years by multiplying the annual cost difference by 6.
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