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Math Help - Linear Applications Word Problem

  1. #1
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    Linear Applications Word Problem

    Problem: The difference between two numbers is 13. Twice the smaller plus three times the larger is 129.
    Answer: 2x+3(x+13) = 129

    I have several questions breaking down this problem:
    1) How do you know which one is the smaller number in the expression above? Do you just assign and compare quantities?
    2) Why does it read (x+13) when the text states the difference between two numbers is 13?

    Thanks for helping me understand this better.
    Last edited by allyourbass2212; July 11th 2012 at 10:52 AM.
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  2. #2
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    Re: Linear Applications Word Problem

    Quote Originally Posted by allyourbass2212 View Post
    Problem: The difference between two numbers is 13. Twice the smaller plus three times the larger is 129.
    Answer: 2x+3(x+13) = 129
    2) Why does it read (x+13) when the text states the difference between two numbers is 13?
    Well (x+13)-x=13. That is difference.

    If x is any number then x+13>x.
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  3. #3
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    Re: Linear Applications Word Problem

    Quote Originally Posted by Plato View Post
    Well (x+13)-x=13. That is difference.

    If x is any number then x+13>x.
    That part makes sense. "The difference between two numbers is 13" when you spell it out is (x+13)-x=13

    But what I am failing to understand is how does that get incorporated into the final expression as (x+13)

    in the expression 2x+3(x+13)=129
    Last edited by allyourbass2212; July 11th 2012 at 11:23 AM.
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    Re: Linear Applications Word Problem

    Quote Originally Posted by allyourbass2212 View Post
    But what I am failing to understand is how does that get incorporated into the final expression as (x+13)
    in the expression 2x+3(x+13)=129
    Well again, x is smaller and x+13 is the larger.
    Two times the smaller plus three times the larger equals 129.
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    Re: Linear Applications Word Problem

    Quote Originally Posted by Plato View Post
    Well again, x is smaller and x+13 is the larger.
    Two times the smaller plus three times the larger equals 129.
    In other words, how the problem is phrased is how we phrase the question.
    "The difference between two numbers is 13" (x+13)-x=13

    Next Phrase. "Twice the smaller plus three times the larger is 129."
    2x+3(x+13) = 129
    2x = smaller number
    PLUS
    3(x+13) = larger number

    In other words, the only reason I know to do small number + larger number, is due to the phrase above. Is this logic correct?
    Last edited by allyourbass2212; July 11th 2012 at 12:08 PM.
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    Re: Linear Applications Word Problem

    2x + 3(x + 13) = 129
    2x + 3x + 13 = 129
    5x = 90
    x = 18

    so, 3x - 2x = 13
    49 - 36 = 13
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