The owner of Firewood To Go is considering buying a hydraulic wood splitter which sells for $50,000.He figures it will cost an additional $150 per cord to purchase and split wood with this machine,while he can sell each cord of split wood for $200. How many cords of wood would he have to split with this machine to make a profit of $50,000?

Question

Quizplus · Accepted Answer

To make a profit of $50,000, the total revenue generated from selling cord of wood must exceed the total cost of purchasing, splitting, and selling that amount of wood.

Let x be the number of cords of wood that need to be split to make a profit of $50,000.

Revenue = Selling price per cord × Number of cords 
Total Cost = Cost per cord × Number of cords + Machine cost

According to the problem, 
Revenue = $200x 
Cost per cord = $150 
Machine cost = $50,000

Total Cost = $150x + $50,000

To make a profit,

Revenue - Total Cost = $50,000

$200x - ($150x + $50,000) = $50,000

$50x = $100,000

x = 2000

Therefore, the owner has to split 2000 cords of wood to make a profit of $50,000.

Option B is the correct answer.

The Owner of Firewood to Go Is Considering Buying a Hydraulic