When I am as old as my father is now, I will be five times as old as my son is now. By then my son will be eight years older than I am now. The combined ages of my father and me are 100 years. How old is my son?

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