Araceli gave away 6 boxes of comic books. Each box had c comic books. After taking 8 comic books from each box, she had 12 comic books left.

Question

Choose the tape diagram that represents the situation.

12
6
c
c
c
c
c

12
c−8
6
6
6
6
6

12
c−8
c−8
c−8
c−8
c−8
c−8

Answer 1

To represent the situation described, we can break it down step by step:

1. Araceli started with 6 boxes of comic books, each containing \(c\) comic books. Therefore, the total number of comic books at the beginning is \(6c\).

2. She took 8 comic books from each box. If each box originally had \(c\) comic books, after taking 8 from each box, each box would have \(c - 8\) comic books left.

3. After taking 8 comic books from each box, she had 12 comic books left. This means that the total number of comic books remaining after she took some from each box is 12.

Given these points, we need a tape diagram that accurately represents:

• The total number of comic books she originally had (\(6c\)),
• The comic books left in each box after taking 8 out (\(c - 8\)),
• The total of 12 comic books left overall.

Now, let's analyze the options:

1. Option 1:

   • 12
   • 6
   • c
   • c
   • c
   • c
   • c

   This option does not represent the situation accurately as it does not show how many comic books were taken away.

2. Option 2:

   • 12
   • \(c - 8\)
   • 6
   • 6
   • 6
   • 6
   • 6

   This is misleading as it implies that there are 6 remaining comic books aside from the total of 12, which doesn’t fit the narrative given that no boxes are shown here.

3. Option 3:

   • 12
   • \(c - 8\)
   • \(c - 8\)
   • \(c - 8\)
   • \(c - 8\)
   • \(c - 8\)
   • \(c - 8\)

   This option represents the total of 12 comic books that were left after taking 8 comic books from each box, indicated by \(c - 8\) for each of the 6 boxes.

Given this breakdown, Option 3 is the most representative of the situation described in the problem, as it shows the total comic books left (12) and the remaining quantities in each box after removing 8 comic books from each.