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

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.