# A boy is three years younger than his sister. If his age three years ago was two-thirds her age at that time, what are their present ages?

Aug 11, 2016

boy is $9$ years old
sister is $12$ years old

#### Explanation:

Let the age of boy be $b$ and the age of his sister be $s$
So given $s = b + 3$
and $b - 3 = \frac{2}{3} \left(s - 3\right)$
or
$3 \left(b - 3\right) = 2 \left(s - 3\right)$
by putting $s = b + 3$ in the equation $3 \left(b - 3\right) = 2 \left(s - 3\right)$
We get
$3 \left(b - 3\right) = 2 \left(b + 3 - 3\right)$
$3 b - 9 = 2 \left(b + 0\right)$
or
$3 b - 9 = 2 b$
or
$3 b - 2 b = 9$
or
$b = 9$-------------boy is $9$ years old
Since $s = b + 3$
or
$s = 9 + 3$
or
$s = 12$ -------------------------sister is $12$ years old