Let’s break this down step by step.
We start with a girl who has as many brothers as sisters. Let’s say the number of brothers in the family is B and the number of sisters is S. According to the girl’s point of view:
- She has S – 1 sisters (because she does not count herself) and B brothers.
This gives us the equation:
B = S – 1 (1)
Now, let’s consider the perspective of a brother. Each brother has half as many brothers as sisters. For a brother:
- He has B – 1 brothers (because he does not count himself) and S sisters.
This gives us the second equation:
B – 1 = 0.5S (2)
Now, we can substitute equation (1) into equation (2). Replace B in equation (2) with the expression from equation (1):
B – 1 = 0.5S
(S – 1) – 1 = 0.5S
S – 2 = 0.5S
To eliminate the decimal, we multiply the entire equation by 2:
2(S – 2) = S
2S – 4 = S
Now, we can solve for S:
2S – S = 4
S = 4
Now that we have S, we can find B using equation (1):
B = S – 1 = 4 – 1 = 3
Therefore, the family consists of 3 brothers and 4 sisters. In conclusion, the solution to this riddle is:
3 brothers and 4 sisters.