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 includes the siding. How many windows must a house have to make the total cost from Company A be less expensive than Company B?

answers:

312 - 12w > 36w

312 + 12w < 36w

12w + 36w > 312

36w - 12w < 312

Answer 1

To determine the inequality that represents the situation, let's define \( w \) as the number of windows.

1. **Cost of Company A**: The cost is $312 for the siding plus $12 for each window. Therefore, the total cost for Company A can be expressed as:
\[
C_A = 312 + 12w
\]

2. **Cost of Company B**: The cost is $36 for each window, and this price includes the siding. Therefore, the total cost for Company B can be expressed as:
\[
C_B = 36w
\]

We want to find the number of windows \( w \) for which the cost from Company A is less expensive than the cost from Company B. This can be expressed with the inequality:
\[
C_A < C_B
\]
Substituting in the expressions for \( C_A \) and \( C_B \):
\[
312 + 12w < 36w
\]

Now we simplify the inequality:
1. Subtract \( 12w \) from both sides:
\[
312 < 36w - 12w
\]
\[
312 < 24w
\]

2. Rearranging gives:
\[
312 < 24w \quad \text{or} \quad 312 > 24w \quad \text{(reversing the inequality)}
\]

To express it in the form that matches one of the given answers:

\[
312 + 12w < 36w
\]

The correct answer from the choices provided is:
\[
\boxed{312 + 12w < 36w}
\]

Answer 2

are you sure

Answer 3

Let's carefully verify the problem and the derived inequality step-by-step to confirm the right inequality that matches the situation.

### Given Information:
1. **Company A**:
- Charges $312 for power-washing the siding of a house.
- Charges $12 for each window.
- Total cost for Company A:
\[
C_A = 312 + 12w
\]

2. **Company B**:
- Charges $36 per window, which includes siding.
- Total cost for Company B:
\[
C_B = 36w
\]

### We need to find when Company A is **less expensive** than Company B:
This can be expressed as:
\[
C_A < C_B
\]
\[
312 + 12w < 36w
\]

### Simplifying the inequality:
1. Subtract \( 12w \) from both sides:
\[
312 < 36w - 12w
\]
\[
312 < 24w
\]

2. Rearranging gives:
\[
312 < 24w \quad \text{or} \quad 312 > 24w \quad \text{(reversed)}
\]

So indeed, the inequality derived correctly is:
\[
312 + 12w < 36w
\]

### Review of Given Answers:
The available answer that matches this situation is:
\[
\boxed{312 + 12w < 36w}
\]

This is confirmed to be correct. Therefore, my initial answer is accurate. Thank you for prompting the clarification!