To find out how many seats are not being used in the auditorium, we need to first determine how many seats are being used by students and then add that to the number of seats being used by teachers.
Let's denote the number of seats used by students as \( S \).
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Calculate the total number of seats used:
- Total seats in the auditorium: 342
- Seats used by teachers: 75
- Thus, seats being used by students is \( S \).
The total number of seats being used is: \[ S + 75 \]
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Calculate the number of empty seats: The number of seats not being used is: \[ \text{Unused seats} = \text{Total seats} - \text{Used seats} \] \[ \text{Unused seats} = 342 - (S + 75) \] \[ \text{Unused seats} = 342 - S - 75 \] \[ \text{Unused seats} = 267 - S \]
To find the exact answer, we need to know the number of seats that the students are using (the value of \( S \)). However, since \( S \) is not provided in your statement, let’s analyze the possible options you’ve given:
Without the value of \( S \), we can't determine the exact number of unused seats. But we can analyze based on different values for \( S \) that will yield one of the choices mentioned.
Choose Different Values of \( S \):
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If \( S = 0 \): \[ \text{Unused seats} = 267 - 0 = 267 \] (Option D)
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If \( S = 75 \): \[ \text{Unused seats} = 267 - 75 = 192 \] (Not an option)
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If \( S = 114 \): \[ \text{Unused seats} = 267 - 114 = 153 \] (Option C)
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If \( S = 204 \): \[ \text{Unused seats} = 267 - 204 = 63 \] (Not an option)
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If \( S = 267 \): \[ \text{Unused seats} = 267 - 267 = 0 \] (Not an option)
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If \( S = 342 \): \[ \text{Unused seats} = 267 - 342 = -75 \] (Not an option)
Conclusion:
From the analysis:
- If students are using 114 seats, then there will be 153 seats not being used (which is option C).
- If students aren’t using any seats, then 267 would be free (option D).
Since the question mentions "Students are using ___ of the seats…” the missing number could indicate it's plausible they are using seats and thus 153 seats being free (option C) is a suitable answer.
Thus, unless additional context about the number of seats students are using is provided, **the answer C. 153 would be correct assuming students occupy 114 seats.