Given:
- The oldest child is twice as old as the youngest child.
- The two middle children are 12 and 15 years old.
- The average age of the children is 13.5.
Let's denote:
- "y" as the age of the youngest child.
The oldest child's age would be "2y" since they are twice as old as the youngest.
Given the average age equation:
(y + 12 + 15 + 2y) / 4 = 13.5
Solving for "y":
3y + 27 = 54
3y = 27
y = 9
So, the youngest child is 9 years old.
