Mary's group of close friends are going to fifth grade in September. All are going to Belleview Elementary and their homerooms will be room 12, 14, or 16. All of her friends but 4 are going o room 12, all but 4 are going to room 14, and all but 4 are going to room 16. Not counting Mary. how many children are in her group of close friends?
To find the total number of children in Mary's group of close friends, we need to add the number of children in each room and then subtract the number of children who are not in any of the rooms mentioned.
Let's assume the number of children going to room 12 is x, the number of children going to room 14 is y, and the number of children going to room 16 is z.
From the given information, we know that all of Mary's friends except for 4 are going to room 12, which can be represented by the equation:
x - 4 = total number of friends in Mary's group (excluding Mary)
Similarly, all but 4 of her friends are going to room 14:
y - 4 = total number of friends in Mary's group (excluding Mary)
And all but 4 of her friends are going to room 16:
z - 4 = total number of friends in Mary's group (excluding Mary)
Since we want to count the total number of friends in Mary's group, we need to find the maximum value of x, y, and z.
Since all friends go to either room 12, 14, or 16, we can assume that the maximum number of friends is in one of the rooms.
If we set x as the maximum, then y and z are at least 4 each. So, y = z = 4.
Substituting these values into the equations:
x - 4 = total number of friends in Mary's group (excluding Mary)
x - 4 = y - 4 = z - 4
x - 4 = 4 - 4 = 0
x - 4 = 0
x = 4
Therefore, the number of children in Mary's group of close friends (excluding Mary) is 4.
Adding Mary, the total number of children in Mary's group of close friends is 4 + 1 = 5.