Answer:
h = 13
Step-by-step explanation:
Let call
i my age
p my father age
h my son age
Then d = p - i is the difference in age between my father and me
From problem statement "When I am as old as my father is now, I will be five times as old as my son is now"
i + d = 5*h = p (1)
And from "By then my son will be eight years older than I am now"
h + d = i + 8 (2)
Finally
i + p = 100 (3)
Solving these equations
From equation (1) d = 5*h - i
Plugging that value in equation (2)
h + ( 5*h - i ) = i + 8 ⇒ h + 5*h - i = i + 8 ⇒ 6*h - 2*i = 8
As 5*h = p
And i + p = 100
i + 5*h = 100 i = 100 - 5*h
6*h - 2*i = 8 i = ( 6*h - 8 )/2
100 - 5*h = ( 6*h - 8 ) /2
200 - 10*h = 6*h - 8
208 = 16*h
h = 208/16
h= 13 years old
