To find the inequality that represents the situation, we first need to express the total cost for both Company A and Company B in terms of the number of windows, which we'll denote as \( x \).
Company A's Cost:
- The base cost for power-washing the siding is $312.
- The cost for windows is $12 per window.
Thus, the total cost for Company A is: \[ \text{Cost}_A = 312 + 12x \]
Company B's Cost:
- The cost per window is $36, and the price includes the siding.
Thus, the total cost for Company B is: \[ \text{Cost}_B = 36x \]
Now we need to find out when Company A's cost is less than Company B's cost. We set up the inequality: \[ 312 + 12x < 36x \]
Next, we will solve this inequality:
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Subtract \( 12x \) from both sides: \[ 312 < 36x - 12x \] This simplifies to: \[ 312 < 24x \]
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Now, divide both sides by 24: \[ \frac{312}{24} < x \]
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Simplifying the left side: \[ 13 < x \] or equivalently: \[ x > 13 \]
This means the house must have more than 13 windows for Company A to be less expensive than Company B.
In conclusion, the inequality that matches the situation is: \[ x > 13 \]