Question

Choose the inequality that matches this situation
Company A charges $312 to power-wash the siding of a house plus $12 for each window. Company B charges $36 per window, and the price includs the siding. How many windows must a house have to make the total cost from Company A be less expensive than Company B?


312 - 12w > 36w

312 + 12w < 36w

12w + 36w > 312

36w - 12w < 312

Answer 1

To determine the inequality that represents the situation, we need to set up an expression for the total cost from both companies and establish when Company A's charges are less than those of Company B.

1. **Cost from Company A**: The total cost is $312 for the siding plus $12 for each window. If we represent the number of windows as \(w\), the cost is:
\[
Cost_A = 312 + 12w
\]

2. **Cost from Company B**: Company B charges $36 per window, and this price includes the siding, so the total cost is:
\[
Cost_B = 36w
\]

Now, we want to find when Company A's cost is less than Company B's cost. Therefore, we need to set up the inequality:
\[
312 + 12w < 36w
\]

Now, let's analyze the provided options:

1. **312 - 12w > 36w**

This is not correct since it's not in the form we've established.

2. **312 + 12w < 36w**

This matches our inequality.

3. **12w + 36w > 312**

This simplifies to \(48w > 312\), which is not the same as what we are looking for.

4. **36w - 12w < 312**

This simplifies to \(24w < 312\), which is not the right form.

Hence, the correct inequality that represents the situation is:
\[
\boxed{312 + 12w < 36w}
\]