Answer: Julia is 48 years
The oldest child is 16 years
The youngest child is 12 years
Step-by-step explanation:
Let x represent the age of the youngest child.
Let y represent the age of the oldest child.
Let x represent Julia's age.
The sum of the ages of Julia and her 2 kids is 76 years. This means that
x + y + z = 76- - - - - - - - - - -1
Julia has 2 children who are 4 years apart in age. This means that
y = x + 4
Julia is four times older than her youngest child. This means that
z = 4x
Substituting z = 4x and y = x + 4 into equation 1, it becomes
x + x + 4 + 4x = 76
6x = 76 - 4 = 72
x = 72/6 = 12
y = x + 4 = 12 + 4
y = 16
z = 4x = 4 × 12
z = 48
