A company manufactures bags from recycled materials. Part of their mission is to raise awareness about environmental issues. To do this, they need to stay in business. To stay in business, they need to be profitable. Help them perform the following calculations to determine the financial health of the company. The company’s cost (in dollars) to manufacture x number of bags is represented by the following algebraic expression: 10,000+0.5x How much is the cost of manufacturing 100 bags? How much is the cost of manufacturing 150 bags? The company sells bags at $150 each. Complete the following table to show how much the company earns for selling different quantities of bags. Number of bags ( x ) Company's earnings 1 2 3 4 100 150 Create an algebraic expression that represents the company’s earnings for selling x number of bags. The company’s profit is calculated by subtracting the manufacturing cost from the earnings. How much is the company’s profit from selling 100 bags? How much is the company’s profit from selling 150 bags? Create an algebraic expression that represents the company’s profit from selling x number of bags. Reveal Answer View Learning Coach Guide
To find the cost of manufacturing 100 bags, we substitute x with 100 in the expression: 10,000 + 0.5x
Cost of manufacturing 100 bags = 10,000 + 0.5(100) = 10,000 + 50 = $10,050
To find the cost of manufacturing 150 bags, we substitute x with 150 in the expression: 10,000 + 0.5x
Cost of manufacturing 150 bags = 10,000 + 0.5(150) = 10,000 + 75 = $10,075
The earnings from selling x number of bags can be calculated by multiplying the number of bags sold (x) by the selling price of each bag ($150).
Algebraic expression for the company's earnings: 150x
To find the company's profit from selling 100 bags:
Profit = Earnings - Cost of manufacturing
Profit = (150 x 100) - (10,000 + 0.5 x 100)
Profit = 15,000 - (10,000 + 50)
Profit = 15,000 - 10,050
Profit = $4,950
To find the company's profit from selling 150 bags:
Profit = Earnings - Cost of manufacturing
Profit = (150 x 150) - (10,000 + 0.5 x 150)
Profit = 22,500 - (10,000 + 75)
Profit = 22,500 - 10,075
Profit = $12,425
Algebraic expression for the company's profit: 150x - (10,000 + 0.5x)