The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. h

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  1. math_celebrity

    math_celebrity Administrator Staff Member

    The total age of three cousins is 48. Suresh is half as old as Hakima and 4 years older than Saad. How old are the cousins?

    Let a be Suresh's age, h be Hakima's age, and c be Saad's age. We're given:
    1. a + h + c = 48
    2. a = 0.5h
    3. a = c + 4
    To isolate equations in terms of Suresh's age (a), let's do the following:
    • Rewriting (3) by subtracting 4 from each side, we get c = a - 4
    • Rewriting (2) by multiply each side by 2, we have h = 2a
    We have a new system of equations:
    1. a + h + c = 48
    2. h = 2a
    3. c = a - 4
    Plug (2) and (3) into (1)
    a + (2a) + (a - 4) = 48

    Group like terms:
    (1 + 2 + 1)a - 4 = 48
    4a - 4 = 48

    Typing this equation into our search engine, we get:
    a = 13 <-- Suresh's age

    This means that Hakima's age, from modified equation (2) above is:
    h = 2(13)
    h = 26 <-- Hakima's age

    This means that Saad's age, from modified equation (3) above is:
    c = 13 - 4
    c = 9 <-- Saad's age

     

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