Answer:the youngest child is 7 years old
Step-by-step explanation:
Let x represent the age of the youngest child.
Let y represent the age of the middle child.
Let z represent the age of the oldest child.
The sum of the ages of three children is 32. It means that
x + y + z = 32 - - - - - - - - - - - 1
The ages of the oldest is twice the age of the youngest. It means that
x = 2z
z = x/2
The two older children differ by 3 years. It means that
y = x - 3
Substituting z = x/2 and y = x - 3 into equation 1, it becomes
x + x - 3 + x/2 = 32
2x - 3 + x/2 = 32
Crossmultiplying,
4x - 6 + x = 64
5x = 64 + 6 = 70
x = 70/5 = 14
z = x/2 = 14/2
z = 7
