Answer: there are 38 men, 76 women and 152 children
Explanation:
Let x represent the number of men in the group.
Let y represent the number of women in the group.
Let z represent the number of children in the group.
The total number of men, women, and children in the group is 266. This means that
x + y + z = 266 - - - - - - - - -1
There are 4 times as many men as children. This means that
z = 4x
x = z/4
There are twice as many woman as children. This means that
z = 2y
y = z/2
Substituting x = z/4 and y = z/2 into equation 1, it becomes
z/4 + z/2 + z = 266
Multiplying through by 4
z + 2z + 4z = 266×4
7z = 1064
z = 152
y = z/2 = 152/2 = 76
x = z/4 = 152/4 = 38