Each child in a family has at least 4 brothers and 3 sisters. What is the smallest number of children the family might have?

If a girl has 4 brothers, then for the boy the number of brothers will be 3. Therefore to satisfy the conditions of brothers, there are 5 male children.

Similarly, if a boy has 3 sisters, then for one of the sisters, the number of sisters she has will be 2. And hence to satisfy the condition for number of sisters, there has to be 4 female children. 

Therefore, the smallest number of children a family can have is 9.