Question

You can purchase an item you need for a project for $10,000 and it has daily operating cost of $500, or you can lease the item for $700 per day. On which day will the purchase cot be the same as the lease cost?

a. Day 5
b. Day 10
c. Day 50
d. Day 100

Answer 1

By setting up an equation comparing the total purchase cost with the operating costs to the lease cost over a number of days, it is determined that the cost will be the same on day 50.

Step-by-step explanation:

To calculate on which day the purchase cost will be the same as the lease cost, we can set up an equation where the purchase cost plus the daily operating costs equals the daily lease cost multiplied by the number of days. If P represents the initial purchase price, D the daily operating cost, L the daily lease cost, and x the number of days, we can create the following equation:

P + (D × x) = L × x

For this specific problem, substituting in the values we have:

$10,000 + ($500 × x) = $700 × x

To find the value of x where both sides of the equation are equal, we solve for x:

• $10,000 + $500x = $700x
• $10,000 = $700x - $500x
• $10,000 = $200x
• x = $10,000 / $200
• x = 50

Therefore, the purchase cost and the lease cost will be the same on day 50.