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Math Help - Worded problem - ages of a lot of people.

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    Worded problem - ages of a lot of people.

    Hi. Recently, my math club teacher assigned me a math problem i could not solve. It appears to be a simple algebraic problem, but i keep getting conflicts about devin's age. Here it is:
    4. Amanda, Anna, Cameron, Emma, Eric, Devin, and Madison are each a different age.
    Figure out the age of each person.
    1) Madison is thirty-five years older than Eric.
    2) Cameron is seventeen years older than Madison.
    3) Amanda is twenty-four years older than Emma.
    4) Emma is eighteen years older than Devin.
    5) The sum of the ages of Amanda and Emma is one hundred fourteen.
    6) The sum of the ages of Madison and Eric is seventy-one.
    7) In fifteen years, Devin's age will be one hundred forty-two less than four times the age of
    Anna.
    8) Devin's age is sixty-six less than three times the age of Anna.


    Can anyone help me? Im only grade 8.
    Last edited by mr fantastic; February 21st 2011 at 07:59 PM. Reason: Re-titled.
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    Quote Originally Posted by pwnagestrike View Post
    Hi. Recently, my math club teacher assigned me a math problem i could not solve. It appears to be a simple algebraic problem, but i keep getting conflicts about devin's age. Here it is:
    4. Amanda, Anna, Cameron, Emma, Eric, Devin, and Madison are each a different age.
    Figure out the age of each person.
    1) Madison is thirty-five years older than Eric.
    2) Cameron is seventeen years older than Madison.
    3) Amanda is twenty-four years older than Emma.
    4) Emma is eighteen years older than Devin.
    5) The sum of the ages of Amanda and Emma is one hundred fourteen.
    6) The sum of the ages of Madison and Eric is seventy-one.
    7) In fifteen years, Devin's age will be one hundred forty-two less than four times the age of
    Anna.
    8) Devin's age is sixty-six less than three times the age of Anna.


    Can anyone help me? Im only grade 8.
    Hi pwnagestrike,

    Let's assign a variable to each name.

    A = Madison
    B = Eric
    C = Cameron
    D = Amanda
    E = Emma
    F = Devin
    G = Anna

    Now, set up the equations based on information given.

    [1] A = B + 35
    [2] C = A + 17
    [3] D = E + 24
    [4] E = F + 18
    [5] D + E = 114
    [6] A + B = 71
    [7] F + 15 = 4(G + 15) - 142
    [8] F = 3G - 66

    Solution:

    Use [7] and [8] to find G = 31 and F = 27.

    Use [1] and [6] to find A = 53 and B = 18.

    Using [2] since you know A, you can find C = 70.

    Using [4] since you know F, you can find E = 45.

    Using [3] since you know E, you can find D = 69.



    Last edited by masters; February 21st 2011 at 12:41 PM.
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