Vedant received two quotes for new carpet for his home. The quote from Company A is $0.15 less per square foot than the quote from Company B. If Vedant plans to buy 1,200 square feet of carpet, how do his total costs from the two companies compare?

Question

Company A is cheaper by $180.
Company B is cheaper by $180.
Company A is cheaper by $8,000.
Company B is cheaper by $8,000.

Answer 1

Let's denote the cost per square foot from Company B as \( x \). According to the problem, the cost per square foot from Company A is \( x - 0.15 \).

Now, let's calculate the total cost for 1,200 square feet from both companies:

• The total cost from Company A: \[ \text{Total Cost A} = 1200 \times (x - 0.15) = 1200x - 180 \]

• The total cost from Company B: \[ \text{Total Cost B} = 1200 \times x = 1200x \]

Now, to find the difference in cost between the two companies: \[ \text{Difference} = \text{Total Cost B} - \text{Total Cost A} = 1200x - (1200x - 180) = 180 \]

Since Company B is the one with the higher cost, we can conclude that:

Company A is cheaper by $180.

Thus, the correct answer is: Company A is cheaper by $180.