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?

$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

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