The same family can look different depending on who is counting it. The trick is not to solve a large equation, but to remember that the speaker is part of the group too.
Brothers and Sisters
Riddle statement
In a family, a boy says:
“I have as many brothers as sisters.”
A girl from the same family says:
“I have twice as many brothers as sisters.”
How many boys and how many girls are there in the family?
Show solution
Solution
Let $b$ be the number of boys and $g$ the number of girls.
The boy has:
$b-1$ brothers; $g$ sisters.
He says he has as many brothers as sisters:
$
b-1=g
$
The girl has:
$b$ brothers; $g-1$ sisters.
She says she has twice as many brothers as sisters:
$
b=2(g-1)
$
From the first equation:
$
b=g+1
$
Substituting into the second:
$
g+1=2g-2
$
Therefore:
$
g=3
$
And then:
$
b=4
$
Answer: there are 4 boys and 3 girls.