To determine the inequality that matches the situation, we need to express the costs of both companies in relation to the number of windows, \( w \).
Company A's cost:
- Fixed cost for siding: $312
- Variable cost for each window: $12
- Total cost for Company A can be expressed as: \[ \text{Cost}_{A} = 312 + 12w \]
Company B's cost:
- Company B charges $36 per window and the price includes the siding.
- Thus, the total cost for Company B can be expressed as: \[ \text{Cost}_{B} = 36w \]
We want the total cost from Company A to be less than the total cost from Company B, so we set up the inequality: \[ 312 + 12w < 36w \]
This means that Company A's cost should be less than Company B's cost. Therefore, the correct inequality that matches the situation is:
\[ 312 + 12w < 36w \]
So the answer is: 312 + 12w < 36w
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