Question

A businesswoman wants to determine the difference between the costs of owning and leasing an automobile. She can lease a car for ​$480 a per month​ (on an annual​ basis). Under this​ plan, the cost per mile is ​$0.04. If she were to purchase the​ car, the fixed annual expense would be ​$4800​, and other costs would amount to ​$0.08 per mile. What is the least number of miles she would have to drive per year to make leasing no more expensive than​ purchasing?

Answer 1

Answer:

$24,000

Explanation:

For computing the least number of miles first we need to calculate the total annual costs for both the plans that are shown below:

For leasing: 

Fixed monthly cost = $480

So, yearly cost = $480 ×  12 = $5,760

Cost per mile = $0.04

Let x is the miles driven

So, the equation would be

= $5,760 + 0.04x ........................... (1)

Now In case of purchasing:

Fixed yearly cost = $4,800

Cost per mile = 0.08

The equation would be

= $4,800 + 0.08x ......................... (2)

Now equate these equations

So,

Cost of leasing ≤ Cost of purchasing

$5,760 + 0.04x ≤ $4,800 + 0.08x

$960 ≤ 0.04x

$24,000 ≤ x