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 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 how many windows must be in the house for Company A to be less expensive than Company B, we need to set up the inequality based on their pricing structures.

**Company A** charges $312 plus $12 for each window:
Cost_A = 312 + 12w

**Company B** charges $36 for each window, and this cost includes the siding:
Cost_B = 36w

We want to find when Company A's cost is less than Company B's cost:
\[ 312 + 12w < 36w \]

Now, let's solve this inequality step-by-step:

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

2. Now, divide both sides by 24 to solve for \(w\):
\[ \frac{312}{24} < w \]
\[ 13 < w \]

This means the number of windows \(w\) must be greater than \(13\).

Thus, a house must have **more than 13 windows** for Company A to be less expensive than Company B.