To find the total number of seventh graders who prefer bananas, we can complete the two-way table step by step.
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Find the total number of seventh graders:
- Total seventh graders = 120.
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Find the total number of eighth graders:
- The total number of apples is 75.
- The total number of bananas is to be determined.
- The total number of oranges is 72.
- We know the total number of eighth graders is the total count of apples, bananas, and oranges.
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Calculate the total number of eighth graders:
- We first calculate the total number of fruits (apples, bananas, oranges).
- Total count (7th + 8th graders) = Apples (75) + Bananas (unknown) + Oranges (72).
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Determine the totals for Bananas:
- From the eighth graders:
- Apples = blank (let this be \( x \))
- Bananas = 32
- Oranges = 45
- Thus, total eighth graders = \( x + 32 + 45 \).
- From the eighth graders:
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Total number of students:
- Since the total of 7th graders + total of 8th graders = Total students:
- \( 120 + (x + 32 + 45) = (75 + \text{Bananas} + 72) \).
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Equations setup:
- Total students = 120 + \( (x + 77) \) = \( 75 + B + 72 \)
- This gives us: \( 120 + x + 77 = 147 + B \)
- Thus: \( x + 197 = 147 + B \)
- Rearranging gives us: \( B = x + 50 \).
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Next we have to calculate \( x \):
- Total number of apples for 7th and 8th graders = 75.
- Since seventh graders have apples = 41:
- For eighth graders \( x = 75 - 41 = 34 \).
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Putting \( x \) into \( B \):
- Thus \( B = 34 + 50 = 84 \).
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The totals for each grade:
- 7th graders' preference: Apples = 41, Bananas = 84.
Therefore, the total number of seventh graders who prefer bananas is 84.