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27 July, 12:29

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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  1. 27 July, 13:19
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    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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