MATH SOLVE

3 months ago

Q:
# A businesswoman wants to determine the difference between the costs of owning and leasing an automobile. She can lease a car for $420 a per month (on an annual basis). Under this plan, the cost per mile is $0.08. If she were to purchase the car, the fixed annual expense would be $4600, and other costs would amount to $0.10 per mile. What is the least number of miles she would have to drive per year to make leasing no more expensive than purchasing?

Accepted Solution

A:

First we need to find the total annual costs for both the plans.

In case of leasing:

Fixed monthly cost = $420

So, yearly cost = 420 x 12 = $5040

Cost per mile = $0.08

For x miles driven, the cost per year for leasing will be = 5040 + 0.08x

In case of purchasing:

Fixed yearly cost = $4600

Cost per mile = 0.10

For x miles driven, the cost per year for leasing will be = 4600 + 0.10x

We want to find for what number of miles will the cost of leasing will be no more expensive than the cost of purchasing.

So,

Cost of leasing ≤ Cost of purchasing

5040 + 0.08x ≤ 4600 + 0.10x

440 ≤ 0.02x

22000 ≤ x

Thus, if if the number of miles driven are equal to or less than 22,000 leasing will be no more expensive than purchasing.

In case of leasing:

Fixed monthly cost = $420

So, yearly cost = 420 x 12 = $5040

Cost per mile = $0.08

For x miles driven, the cost per year for leasing will be = 5040 + 0.08x

In case of purchasing:

Fixed yearly cost = $4600

Cost per mile = 0.10

For x miles driven, the cost per year for leasing will be = 4600 + 0.10x

We want to find for what number of miles will the cost of leasing will be no more expensive than the cost of purchasing.

So,

Cost of leasing ≤ Cost of purchasing

5040 + 0.08x ≤ 4600 + 0.10x

440 ≤ 0.02x

22000 ≤ x

Thus, if if the number of miles driven are equal to or less than 22,000 leasing will be no more expensive than purchasing.