To determine which inequality matches the situation, let's first express the total costs for both companies in terms of the number of windows, denoted as \( w \).
Company A:
- The cost is a fixed charge of $312 for power-washing the siding plus $12 for each window. Therefore, the total cost for Company A can be expressed as: \[ \text{Cost}_A = 312 + 12w \]
Company B:
- Company B charges $36 per window, and this includes the siding. Thus, the total cost for Company B is: \[ \text{Cost}_B = 36w \]
We want to find the number of windows \( w \) such that the total cost from Company A is less expensive than Company B. This can be expressed mathematically as: \[ \text{Cost}_A < \text{Cost}_B \]
Substituting the cost expressions: \[ 312 + 12w < 36w \]
To simplify this inequality:
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Subtract \( 12w \) from both sides: \[ 312 < 36w - 12w \] \[ 312 < 24w \]
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Divide both sides by 24: \[ 13 < w \] or equivalently, \[ w > 13 \]
This tells us that for the cost from Company A to be less than that from Company B, the house must have more than 13 windows.
Now, looking at your provided inequalities:
- 312 - 12w > 36w (not correct; rearranging would lead to a wrong relationship)
- 312 + 12w < 36w (this is correct; it matches what we derived)
- 12w + 36w > 312 (not correct; simplifies to 48w > 312, but this is not what we need)
- 36w - 12w < 312 (not directly useful since it does not compare the costs correctly)
The correct inequality corresponding to the situation is: 312 + 12w < 36w
This shows that the cost from Company A must be less than that from Company B for the number of windows \( w \).
2 answers