Let's break down the costs for both cleaning companies.
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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.
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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 \( w \):
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Subtract \( 12w \) from both sides: \[ 312 = 36w - 12w \] \[ 312 = 24w \]
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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.