Question

The home cleaning company charges $312 to power wash the siding of the house plus $12 each window power clean charges $36 per window and the price includes power washing the siding. How many windows must a house have to make the total cost each cleaning company the same windows

Answer 1

Let's break down the costs for both cleaning companies.

1. **Home cleaning company:**

- Cost for power washing the siding = $312
- Cost for each window = $12
- Total cost for the home cleaning company can be calculated as:
\[
\text{Total cost} = 312 + 12w
\]
where \( w \) is the number of windows.

2. **Other cleaning company:**

- Cost includes power washing the siding and cleaning windows, which is $36 per window.
- Total cost for the other cleaning company can be represented as:
\[
\text{Total cost} = 36w
\]

Now, we need to set the equations equal to each other to find the number of windows (\( w \)) at which both costs are the same:
\[
312 + 12w = 36w
\]

Now, let's solve for \( w \):

1. Subtract \( 12w \) from both sides:
\[
312 = 36w - 12w
\]
\[
312 = 24w
\]

2. Divide both sides by 24:
\[
w = \frac{312}{24}
\]
\[
w = 13
\]

Therefore, a house must have **13 windows** for the total cost of each cleaning company to be the same.