Let x be the quantity of Coke. The father had x/4, while each of the rest of the family had (3x/4)/(n-1) where n is the size of the family including the father. Therefore, since the father's proportion was 3 times the equal quantities of the other family members:
x/4=3(3x/4)/(n-1)
Multiply through by 4(n-1): x(n-1)=9x, divide both sides by x: n-1=9, so n=10.
So there are 9 family members in the rest of the family.
We don't know who the other family members are but one family arrangement could be:
Father, mother, 4 kids, father's parents, mother's parents.
EXAMPLE
If there were 12 cans of Coke, then dad had 3 cans, and 9 cans were distributed equally to the other 9 members of the family (one can each).