You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet.

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You are purchasing carpeting for an office building. The space to be carpeted is 30 feet by 50 feet. Company A charges $2.99 per square foot plus a $200 installation charge. Company B charges $19.99 per square yard plus a $500 installation charge. What is the best deal?

Did you notice the word snuck in on this problem? Company B is given in square yards, not feet. Let's convert their price to square feet to match company A.

Company B conversion:
Since we have 1 square yard = 3 feet * 3 feet = 9 square feet, we need to solve the following proportion:
$19.99/square yard * 1 square yard/9 feet = $19.99 square yard / 9 feet = $2.22 / square foot.

Now, let's set up the cost equations C(s) for each Company in square feet (s)

• Company A: C(s) = 200 + 2.99s
• Company B: C(s) = 500 + 2.22s

The problem asks for s = 30 feet * 50 feet = 1500 square feet. So we want to calculate C(1500)

Company A:
C(1500) = 200 + 2.99(1500)
C(1500) = 200 + 4485
C(1500) = 4685

Company B:
C(1500) = 500 + 2.22(1500)
C(1500) = 500 + 3330
C(1500) = 3830

Since Company B has the lower cost per square foot, they are the better buy.