SOLUTION: My brother says he has an equal number of brothers and sisters and my sister says she has twice as many brothers than she has sisters. How many boys and how many sisters.

Suppose there are B boys and G girls.

Your brother has B-1 brothers.  [He is not his own brother]
Your brother has G sisters.

B-1 = G

Your sister has B brothers
Your sister has G-1 sisters. [She is not her own sister]

B = 2(G-1)

So the system of equations is

B-1 = G
B = 2(G-1)

Substitute 2(G-1) for B in the first equation:

2(G-1)-1 = G
  2G-2-1 = G
    2G-3 = G
       G = 3

Substitute 3 for G in

B-1 = G
B-1 = 3
  B = 4

There are 4 boys and 3 girls.

Edwin