Answer:
The age of the youngest child = x = 6 years
The age of middle child = y = 8 years
The age of the oldest child = z = 12 years
Explanation:
Let us represent:
The age of the youngest child = x
The age of middle child = y
The age of the oldest child = z
The sum of the ages of the children is 26.
Hence: x + y + z = 26...... Equation 1
The oldest is 4 years older than the middle
z = 4 + y
The youngest child is 2 years younger than the middle child
x = y - 2
Hence, we substitute 4 + y for z and y - 2 for x in Equation 1
x + y + z = 26...... Equation 1
y - 2 + y + 4 + y = 26
y + y + y -2 +4 = 26
3y + 2 = 26
Subtract 2 from both sides
3y + 2 - 2 = 26 - 2
3y = 26 - 2
3y = 24
y = 24/3
y = 8
Solving for x
x = y - 2
x = 8 - 2
x = 6
Solving for z
z = 4 + y
z = 4 + 8
z = 12
Therefore:
The age of the youngest child = x = 6 years
The age of middle child = y = 8 years
The age of the oldest child = z = 12 years