9. Peter has three times as many sisters as brothers. His sister Louise has twice as many sisters as brothers. How many children are there in the family?
A 15
B 13
C 11
D 9
E 5
Solution: B
Suppose Peter has $b$ brothers and hence $3 b$ sisters. So, including Peter, there are $b+1$ boys and $3 b$ girls in the family. So Louise has $b+1$ brothers and $3 b-1$ sisters. Since Louise has twice as many sisters as brothers, $3 b-1=2(b+1)$. This equation is equivalent to $3 b-1=2 b+2$. So $b=3$ and there are 4 boys and 9 girls in the family, making 13 children altogether.