## 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.

Question

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?

in progress 0
2 weeks 2021-09-27T02:54:15+00:00 1 Answer 0

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