Answer:
4 brothers and 3 sisters
Step-by-step explanation:
Let x be the number of brothers and y be the number of sisters in the family.
1. Each brother has x-1 brothers and y sisters. If each brother has as many sisters as brothers, then

2. Each sister has y-1 sisters and x brothers. If each sister has twice as many brothers as she has sisters, then

3. Solve the system of two equations:

Then

Answer:
Unless im being completely braindead right now there isn't a whole number that works with this. When simplified its 5/2 or 2.5 but because it isn't an actual whole number (like 2, 4 and 6) they don't count.