edant 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 price per square foot from Company B as \( x \). According to the problem, the price per square foot from Company A is \( x - 0.15 \).

Now, we can calculate the total costs for 1,200 square feet of carpet from both companies:

• Total cost from Company A:
  \[ \text{Cost from A} = 1,200 \times (x - 0.15) = 1,200x - 180 \]

• Total cost from Company B:
  \[ \text{Cost from B} = 1,200 \times x = 1,200x \]

Next, we compare the total costs:

\[ \text{Cost from B} - \text{Cost from A} = 1,200x - (1,200x - 180) = 180 \]

This calculation shows that Company A is cheaper than Company B by $180.

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