Final answer:
To find when the lease cost equals the purchase cost, we calculate that it will take 60 days for the lease cost of $200 per day to equal the purchase cost of a $6,000 investment plus a $100 daily cost.
Step-by-step explanation:
To determine after how many days the lease cost of an item will be the same as the purchase cost, we need to set up an equation where the total costs of leasing and purchasing are equal. Let's denote the number of days as d.
The total lease cost after d days will be $200 × d. On the other hand, the total purchase cost after d days will include the initial investment cost plus the daily cost incurred, which is $6,000 + $100 × d.
Now we can set up the equation as follows:
$200 × d = $6,000 + $100 × d.
Simplifying the equation by subtracting $100 × d from both sides, we get:
$200 × d - $100 × d = $6,000,
$100 × d = $6,000.
Finally, divide both sides by $100 to solve for d:
d = $6,000 / $100,
d = 60 days.
Therefore, it will take 60 days for the lease cost to be the same as the purchase cost.