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Use the table to answer the question.

This table tracks the fruit preference of 7th and 8th students
7th graders : apples=44, Banana= blank, Oranges=blank Total 120
8th graders: Apples= blank, Banana=35, Oranges=46, Total= blank
Totals Vertical: Apples=72, Banana= blank, Oranges=71, Total= Blank
Constructing the two-way table, what is the total number of seventh graders who prefer bananas?

(1 point)
Responses

69
69

86
86

25
25

51
51
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1 answer

To find the number of 7th graders who prefer bananas, we need to use the information from the table.

We know that:

  • Total 7th graders = 120
  • Total apples preference among 7th graders = 44
  • Total oranges preference among 7th graders = blank
  • Total for all fruits among 7th graders should equal 120.

Let's denote:

  • Number of 7th graders who prefer bananas = \(B\)
  • Number of 7th graders who prefer oranges = \(O\)

Thus, we can express the total fruit preferences for 7th graders as: \[ 44 + B + O = 120 \]

Now we can find the total number of 7th graders who prefer oranges, which contributes to the totals for the 8th graders.

From the totals:

  • Total apples = 72 (implying 8th graders prefer apples = \(72 - 44\) = \(28\))
  • Total oranges = 71 (implying 7th graders and 8th graders combined must be 71).

The 8th graders who prefer oranges = 46. Thus:

  • \(O + 46 = 71\)
  • Solving for \(O\) gives \(O = 71 - 46 = 25\).

Now we can substitute \(O\) back into the 7th graders equation: \[ 44 + B + 25 = 120 \] This simplifies to: \[ B + 69 = 120 \] Therefore, \(B = 120 - 69 = 51\).

The total number of seventh graders who prefer bananas is 51.

So the answer is: 51