A father is 60 years old and his son is half his age. How old was the boy when his father was four times his age?

Question

A father is 60 years old and his son is half his age. How old was the boy when his father was four times his age?

 

Answer 1

Since the son is 1/2 the father's age,  The son is 1/2 of 60, or 30 years old

 

Let   N = the number of years ago when father was 4 times his son's age 

 

That would have occurred (30 - N) years ago, since the boy is 30.  The boy would have been 30 - N, and the dad would have been 60 - N

 

We can construct the following equation:

 

    4 • (boys age) = Father's age

    4•(30 - N) = 60 - N

    120 - 4N = 60 - N

    120 - 60 = -N + 4n

     60 = 3N

      N = 20

 

So 20 years ago

 

     The son was 30 - 20 = 10 years old

     The father was 60 - 20 =40 years old

 

40 = 10 times 4

 

 

Answer 2

The father is currently 60 years old and his son is half his age, so his son is currently 30 years old.  Let x be the number of years ago that the father was 4 times as old as his son.  So the father was 60-x years old and the son was 30-x years old We want:

 

  (60-x) = 4·(30-x)

  60-x = 120 - 4x

  3x = 60

 

  x = 20 years ago

 

So the boy was 30-20 = 10 years old.  The father was 60 - 20 = 40 years old.  10*4 = 40, so it checks.