Sunae's group of close friends are going to fifth grade in September. All are going to Belleview Elementary and their homerooms will be rooms 12, 14, or 16. All of her friends but 4 are going to room 12, all but 4 are going to room 14, and all but 4 are going to room 16. Not counting Sunae, how many children are in her group of close friends?

Hint:

Try to see if 2 friends to each of rooms 12, 14 and 16 works.

12

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The answer is 6.

The rooms could just have well been labeled A, B, C.
6-4=2 Room A
6-4=2 Room B
6-4=2 Room C

2+2+2=6

or since all but 4 are going into each room, the 4 going into other rooms are split equally into 2 and 2.

To answer this question, we need to find out how many friends are going to each of the three homerooms: rooms 12, 14, and 16. We know that all of Sunae's friends but 4 are going to room 12, all but 4 are going to room 14, and all but 4 are going to room 16.

Let's break this down step by step:

1. Start with the total number of friends in Sunae's group (including herself). Let's call this number "x".

2. Subtract 4 from x to find the number of friends going to room 12.

3. Subtract another 4 from x to find the number of friends going to room 14.

4. Subtract 4 again from x to find the number of friends going to room 16.

5. Now, we want to determine how many friends are going to each room without counting Sunae. So we subtract 1 from the number of friends going to each room.

6. Finally, add up the number of friends going to each room (subtracting 1 from each) to get the total number of friends in Sunae's group (excluding Sunae herself).

Let's solve it step by step:

1. Total number of friends (including Sunae) = x

2. Number of friends going to room 12 = x - 4

3. Number of friends going to room 14 = x - 4 - 4 = x - 8

4. Number of friends going to room 16 = x - 4 - 4 - 4 = x - 12

5. Number of friends in room 12 (excluding Sunae) = x - 4 - 1 = x - 5

6. Number of friends in room 14 (excluding Sunae) = x - 8 - 1 = x - 9

7. Number of friends in room 16 (excluding Sunae) = x - 12 - 1 = x - 13

8. Total number of friends in Sunae's group (excluding Sunae herself) = (x - 5) + (x - 9) + (x - 13)

Now we can find the value of "x" by looking at the information given in the question.