Suppose that the purchase price for a piece of equipment is $12,000, with operational costs of $400 per day. If the same equipment can be leased for $800 per day (inclusive of operational costs), after how many days will the lease cost equal the purchase cost?

after 30 days lease cost equal the purchase cost

Explanation:

Data provided in the question:

Purchasing cost of the equipment = $12,000

operational costs = $400 per day

Lease amount for the equipment = $800 per day

Now,

Let the number of days after which lease cost equal the purchase cost be 'x'

therefore,

Total cost when purchased = $12,000 + $400x

Total cost when equipment is leased = $800x

therefore,

for equal costs

$12,000 + $400x = $800x

or

$800x - $400x = $12,000

or

$400x = $12,000

or

x = 30 days

hence,

after 30 days lease cost equal the purchase cost