The tires on Mavis’ car will have to be replaced when they each have 160,000 km of wear on them. If new tires cost $140.00 each, what is the total cost of the wear on Mavis’ tires for a year in which she drives 25,000 km?
The Correct Answer and Explanation is:
To find the total cost of the tire wear for the year when Mavis drives 25,000 km, we need to calculate how much of the tire’s life was used up and what portion of the tire’s cost corresponds to that usage.
Step-by-step solution:
- Total lifespan of one tire = 160,000 km
- Cost of one tire = $140.00
- Distance Mavis drives in a year = 25,000 km
- Number of tires on the car = 4
Step 1: Calculate cost per km for one tire
Cost per km for one tire=$140.00160,000 km=0.000875 dollars/km\text{Cost per km for one tire} = \frac{\$140.00}{160,000\ \text{km}} = 0.000875\ \text{dollars/km}Cost per km for one tire=160,000 km$140.00=0.000875 dollars/km
Step 2: Multiply by 25,000 km to get yearly wear cost per tire
0.000875×25,000=21.875 dollars per tire per year0.000875 \times 25,000 = 21.875\ \text{dollars per tire per year}0.000875×25,000=21.875 dollars per tire per year
Step 3: Multiply by 4 tires
21.875×4=87.50 total dollars of wear for all tires in one year21.875 \times 4 = 87.50\ \text{total dollars of wear for all tires in one year}21.875×4=87.50 total dollars of wear for all tires in one year
✅ Final Answer:
$87.50\boxed{\$87.50}$87.50
explanation:
To understand how much Mavis spends on tire wear over the year, we first consider the lifespan and cost of a tire. Each tire is designed to last for 160,000 kilometers and costs $140.00. That means the cost of using up each kilometer of one tire’s lifespan is calculated by dividing the cost by the total distance: $140.00 divided by 160,000 km equals $0.000875 per kilometer.
Mavis drives 25,000 kilometers in one year. If we multiply the cost per kilometer ($0.000875) by the number of kilometers she drives (25,000), we find that each tire incurs $21.875 worth of wear. Since her car uses four tires, we multiply this annual wear cost by four: $21.875 multiplied by 4 gives $87.50.
This means that even though she does not actually replace the tires each year, she is using up $87.50 worth of the tires’ value over the course of 25,000 kilometers. It helps in understanding how much value is lost from the tires annually based on her driving distance, and it can also help in budgeting for tire replacement in the future. This cost is often considered part of the annual operating or depreciation cost of maintaining a vehicle.
