Question

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?

Answer 1

answers are:

312 - 12w > 36w

312 + 12w < 36w

12w + 36w > 312

36w - 12w < 312

Answer 2

pick an answer.

Answer 3

To determine how many windows a house must have for Company A to be cheaper than Company B, we can set up the following cost equations for both companies:

- For Company A:
\[
\text{Cost}_A = 312 + 12w
\]
where \( w \) is the number of windows.

- For Company B:
\[
\text{Cost}_B = 36w
\]

We want to find the number of windows \( w \) such that:
\[
\text{Cost}_A < \text{Cost}_B
\]
This can be written as:
\[
312 + 12w < 36w
\]

Now, we can solve this inequality step-by-step.

1. Subtract \( 12w \) from both sides:
\[
312 < 36w - 12w
\]
This simplifies to:
\[
312 < 24w
\]

2. Divide both sides by 24:
\[
\frac{312}{24} < w
\]
Simplifying the left side:
\[
13 < w
\]
or
\[
w > 13
\]

This means that the house must have more than 13 windows for the total cost from Company A to be less expensive than that from Company B.

Thus, the minimum number of windows for Company A to be cheaper is \( \mathbf{14} \).

Answer 4

Let's analyze the information you've provided regarding the inequalities in order to evaluate the comparison of costs between Company A and Company B.

Since we need to find how many windows \( w \) must be installed for Company A to be cheaper than Company B, we can start from the correct setup.

The costs we have previously established are:

- For **Company A**:
\[
\text{Cost}_A = 312 + 12w
\]
- For **Company B**:
\[
\text{Cost}_B = 36w
\]

We need to establish the inequality:
\[
312 + 12w < 36w
\]

Now let's manipulate this inequality step by step:

1. **Isolate w** by subtracting \( 12w \) from both sides:
\[
312 < 36w - 12w
\]
This simplifies to:
\[
312 < 24w
\]

2. **Divide both sides by 24** to solve for \( w \):
\[
\frac{312}{24} < w
\]
Simplifying the left side gives:
\[
13 < w
\]
or equivalently:
\[
w > 13
\]

This indicates that for Company A's total cost to be less than Company B's total cost, the number of windows \( w \) must be greater than 13. Therefore, the smallest integer that satisfies this is:
\[
w = 14
\]

Thus the correct answer remains: **A house must have at least 14 windows** for Company A to be less expensive than Company B.

If you have additional conditions or variations in the inequalities you want to explore, please let me know!

Answer 5

Based on the analysis, the answer is:

**14 windows**

A house must have at least 14 windows for the cost from Company A to be less expensive than the cost from Company B.