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 + 12 w < 36w
12x + 36w > 312
36w - 12w < 312

Answer 1

To determine the inequality that matches the situation, we need to set up the cost functions for both companies.

For Company A:
- The cost to power-wash the siding is $312.
- The cost to power-wash each window is $12.
- Therefore, the total cost for Company A can be expressed as:
\[
\text{Cost}_A = 312 + 12w
\]
where \( w \) is the number of windows.

For Company B:
- The cost for each window is $36, and this cost includes the siding.
- Thus, the total cost for Company B is:
\[
\text{Cost}_B = 36w
\]

Now, we need to find the number of windows \( w \) such that Company A's cost is less than Company B's cost:
\[
312 + 12w < 36w
\]

This inequality simplifies to:
\[
312 < 36w - 12w
\]
\[
312 < 24w
\]

Now let's write it in the original format:
\[
312 + 12w < 36w
\]

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