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