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

So if he's half of 60 that's 30.
If he's 4x his current age he was 120.
Half of 120 is 60.
I want to say he was 60.
Here's another theory of mine:
1*4=4
Let's go by 10s,
X(boy)*(stated in problem) =fathers age
10*4=40
20*4=80
30*4=120

C'Mon why would he, the father be 120
I sort of doubt 80
I don't doubt 40
Of course this is my thinking it may or may be correct but with Mathematical solving can it be determined.

Answer 2

Now, father is 60 years old and his son is half his age
so son's age is 60/2 = 30 years old
let x = the number of years back then when his father was four times his age
4(30 - x) = 30
120 - 4x = 30
 4x = 80
   x = 20

so 20 years back then
son's age = 30 - 20 = 10
father's age = 60 - 20 = 40

answer
the son's age was 10 when his father was 40 (four times his age)