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    Word Problems: Age Related


    The majority of age problems include the present ages of two or more persons, in addition to their ages at particular past and/or future times.  The key to solving these problems is to translate the verbiage into equations using subscripted variables.

    Example #1:

    Brian is presently four times older than Sam.  Six years later, he will be twice as old as Sam.  How old are Brian and Sam?

    Solution #1:

    Using subscripts variables of BP and SP to denote the age of Brian and Sam at the present time, we may construct the following table:

    Present Age Age Six Years Later
    Brian BP BP + 6
    Sam SP SP + 6


    Since Brian is presently four times the age of Sam:

    BP = 4SP

    Knowing that Brian will be twice as old as Sam in six years:

    BP + 6 = 2(SP + 6)

    Substituting     BP = 4SP:

    4SP + 6 = 2(SP + 6)

    4SP + 6 = 2SP + 12

    4SP − 2SP =  12 − 6

    2SP = 6

    SP = 3 years old

    Since     BP = 4SP:

    BP = 4(3) Years Old

    BP = 12 years old
    Example #2:

    A year ago, John was three times as old as Larry.  A year later, he was twice as old as Larry.  How old are John and Larry?

    Solution #2:

    Using subscripts variables of JP and LP to denote the age of Brian and Sam at the present time, we may construct the following table:

    Present Age Age Year Ago Ago Year Later
    John JP JP − 1 JP + 1
    Larry LP LP − 1 LP + 1


    Since John was three times as old as Larry a year ago:

    JP − 1 = 3(LP − 1)

    JP − 1 = 3LP − 3

    JP = 3LP − 2

    Knowing that John will be twice as old as Brian in one year:

    JP + 1 = 2(LP + 1)

    Substituting     JP = 3LP − 2:

    (3LP − 2) + 1 = 2(LP + 1)

    3LP − 1 = 2LP + 2

    3LP − 2LP =  2 + 1

    LP = 3 years old

    Since     JP = 3LP − 2:

    JP = 3LP − 2

    JP = 3(3) − 2 years old

    BP = 7 years old


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