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?

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

Answers ( )

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    2021-09-27T02:56:05+00:00

    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

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