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 chilren are in her group of close friends? Please explain
To find the number of children in Sunae's group of close friends, we need to determine how many children are going to each room and then add them all together.
Let's start with the information given:
- All of her friends but 4 are going to room 12.
- All but 4 are going to room 14.
- All but 4 are going to room 16.
Let's assume the number of children going to room 12 is x, the number going to room 14 is y, and the number going to room 16 is z.
From the information given, we can form three equations:
1) x - 4 = number of friends going to room 12
2) y - 4 = number of friends going to room 14
3) z - 4 = number of friends going to room 16
We also know that the total number of friends in Sunae's group is x (room 12) + y (room 14) + z (room 16), which we need to find.
To solve the problem and find the values of x, y, and z, we can use a system of equations. We'll add 4 to both sides of each equation to get rid of the subtracted 4:
1) x - 4 + 4 = number of friends going to room 12 + 4
x = number of friends going to room 12 + 4
2) y - 4 + 4 = number of friends going to room 14 + 4
y = number of friends going to room 14 + 4
3) z - 4 + 4 = number of friends going to room 16 + 4
z = number of friends going to room 16 + 4
Now we have three equations:
x = number of friends going to room 12 + 4
y = number of friends going to room 14 + 4
z = number of friends going to room 16 + 4
However, we don't know the values of x, y, and z yet. We need more information from the given statement.
The statement says, "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." This means that the remaining 4 children (excluding Sunae) are not going to any of these rooms.
From this, we can conclude that:
The number of friends going to room 12 + 4 + 4 = total number of children in Sunae's group (including Sunae)
Therefore, the total number of children in Sunae's group of close friends is (x + 4) + (y + 4) + (z + 4) = x + y + z + 12.
We need more information to find the values of x, y, and z.