#### Answer

His age is $30$ years old while his sister's age is $21$ years old.

#### Work Step by Step

1. Finding the person's age
Let $x = $ the person's age
(person's age) + (sister's age) $= 51$
$(x) + (x - 9) = 51$
$2x - 9 = 51$
$2x = 60$
$x = \frac{60}{2}$
$x = 30$ years old
2. Finding his sister's age
Let $S =$ his sister's age
$S = x - 9$
$S = 30 - 9$
$S = 21$ years old