How many children are there in a family where each girl has as many brothers as sisters....

Question

How many children are there in a family where each girl has as many brothers as sisters, but each boy has twice as many sisters as brothers?

 

Please explain step by step. Thanks.

Answer 1

Let the number of girls be X, and the number of boys be Y. Then, for a girl, there is X-1 sisters (not including herself) and Y brothers.

 

Also, we know for each girl,

 

Y=X-1

 

since from her point-of-view, there are the same number of sisters as brothers.

 

From the boy's perspective, not including himself, there are Y-1 brothers and X sisters.

 

Also, we know that for each boy,

 

2(Y-1)=X

 

since from his point-of-view, there are twice as many sisters than brothers. 

 

We have 2 equations and 2 unknowns, so substituting the 2nd equation into the 1st, we get

 

Y = 2(Y-1)-1 = 2Y-3

 

so

 

Y=2Y-3

Y+3=2Y

Y=3

 

We use the first equation and see

Y = X-1 =3

X=4

 

So there are 4 girls and 3 boys.