Current ages:
Let Kaylan's present age be x years
Since his age is a third of his mother's present age:
mother's age * (1/3) = Kaylan's age
mother's age * (1/3) = x
mother's age = 3x [multiplying both sides by 3]
Kaylan's mother's age would be 3x years
Their ages 6 years ago:
Kaylan's age: x-6 years
Mother's age: 3x-6 years
We are told that mother's age was 5 times Kaylan's age, 6 years ago. So,
5*(Kaylan's age 6 years ago) = (Mother's age 6 years ago)
replacing the values
5(x - 6) = 3x-6
5x - 30 = 3x-6
2x - 30 = -6 [subtracting 3x from both sides]
2x = 24 [adding 30 on both sides]
x = 12 [dividing both sides by 2]
Hence, x = 12
Kaylan's present age(x) = 12 years
Mother's present age(3x) = 3*12 = 36 years
