A man is four times as old as his daughter. Six years ago he was ten times as old as his daughter. How old are they now?

Answer 1

Daughter's age now = x
Man's age now = 4x

Six years ago, she was x-6 and he was 6x-6
4x-6 = 10(x-6)

easy to solve for x

Answer 2

m = man´s present age

d = daughter´s present age

A man is four times as old as his daughter means:

m = 4 d

Six years ago he was m - 6 years old , daughter was d - 6 ears old

Six years ago he was ten times as old as his daughter means:

m - 6 = 10 ( d - 6 )

Replace m with 4 d in this equation

4 d - 6 = 10 ( d - 6 )

4 d - 6 = 10 d - 60

Subtract 4 d to both sides

- 6 = 6 d - 60

Add 60 to both sides

54 = 6 d

6 d = 54

Divide both sides by 6

d = 9

m = 4 d = 4 ∙ 9 = 36

Now he is 36 years old

Proof:

m / d = 36 / 9 = 4

Six years ago he was 36 - 6 = 30 years old and

Six years ago daughter was 9 - 6 = 3 years old

30 / 3 = 10