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 $$\square$$ over six years.
(Round to the nearest dollar as needed.)
Answer (2)
Calculate the annual expense for Car A: 30 , 000 miles × $0.98/ mile = $29 , 400 .
Calculate the annual expense for Car B: 30 , 000 miles × $0.70/ mile = $21 , 000 .
Find the difference in annual expenses: $29 , 400 − $21 , 000 = $8 , 400 .
Calculate the total difference over six years: $8 , 400 × 6 = $50 , 400 .
Explanation
Calculate total cost per mile First, we need to calculate the total cost per mile for each car. For Car A, the total cost per mile is given as $0.98. For Car B, the total cost per mile is given as $0.70.
Calculate annual expense Next, we calculate the annual expense for each car by multiplying the total cost per mile by the number of miles driven per year (30,000 miles).
Annual expense for Car A Annual expense for Car A: 30 , 000 × 0.98 = $29 , 400 .
Annual expense for Car B Annual expense for Car B: 30 , 000 × 0.70 = $21 , 000 .
Difference in annual expenses Now, we find the difference in annual expenses between Car A and Car B: $29 , 400 − $21 , 000 = $8 , 400 .
Total difference over six years Finally, we calculate the total difference in expenses over six years by multiplying the annual difference by 6: $8 , 400 × 6 = $50 , 400 .
Final Answer Therefore, the total annual expense for Car A exceeds that of Car B by $50 , 400 over six years.
Examples
Understanding the long-term costs of owning a car can help you make informed financial decisions. For example, if you are deciding between two cars and know the average operating and ownership costs per mile, you can calculate the total cost over several years. This can help you budget effectively and choose the more economical option, especially if you drive a lot. This type of calculation is also useful in business for managing fleet expenses and optimizing transportation costs.
The total annual expense for Car A exceeds that of Car B by $50,400 over six years, based on the assumption that Car B's total cost per mile is $0.70. This was calculated by determining the annual expenses for each car and finding the difference over six years. Ensure to use the correct costs for Car B to verify the exact difference.
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