The difference in age between a girl and her younger sister is 4 years. The younger sister in turn is 4 years older than her brother. The sum of the ages of the younger sister and the brother is 16. How old are the three children?
Given :
The difference in age between a girl and her younger sister is 4 years.
The younger sister, in turn, is 4 years older than her brother.
The sum of the ages of the younger sister and the brother is 16.
To do :
We have to find the ages of the children.
Solution :
Let the age of the younger sister be x
This implies,
The age of the girl $= x+4$
The age of the brother $= x-4$
The sum of the ages of the younger sister and her brother $= 16$
Therefore,
$x+(x-4) = 16$
$2x-4 = 16$
$2x = 16+4$
$2x=20$
$x=\frac{20}{2}$
$x=10$
The age of the younger sister is 10 years.
The age of the younger brother is $10-4=6$ years.
The age of the girl is $10+4=14$ years.
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