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Math Help - Word problems involving Quadratic systems...

  1. #1
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    Word problems involving Quadratic systems...

    The printed area of a rectangular poster is 704 sq inches... the printed area plus the area of the margins is 1200 sq inches find the dimension of the poster if each of the margins is 4" wide...

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  2. #2
    MHF Contributor Quick's Avatar
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    Quote Originally Posted by ^_^Engineer_Adam^_^ View Post
    The printed area of a rectangular poster is 704 sq inches... the printed area plus the area of the margins is 1200 sq inches find the dimension of the poster if each of the margins is 4" wide...

    !
    704=w*l

    Adding the printed margins we get: (w+8)*(l+8)=1200

    Use Foil: w*l+8(w+l)+64=1200

    subtract 64 from both sides: w*l+8(w+l)=1136

    Subtract this equation by the first equation: w*l+8(w+l)-w*l=1136-704

    thus: 8(w+l)=432

    divide: w+l=54

    Now you can choose between literally infinite possibilities for dimensions.

    Edit: Apparently not I hope you haven't turned this in Adam...
    Last edited by Quick; October 4th 2006 at 02:19 AM.
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  3. #3
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    Hello, ^_^Engineer_Adam^_^!

    The printed area of a rectangular poster is 704 in.
    The printed area plus the area of the margins is 1200 in.
    Find the dimension of the poster if each of the margins is 4" wide.
    Code:
          : 4 :  - x -  : 4 :
        - * - - - - - - - - * -
        4 |                 | :
        - |   * - - - - *   | :
        : |   |         |   | : 
        : |   |         |   | :
        y |   |y        |   | y+8
        : |   |         |   | :
        : |   |    x    |   | :
        - |   * - - - - *   | :
        4 |                 | :
        - * - - - - - - - - * -
          : - - - x+8 - - - :

    The length of the printed area is x.
    The height of the printed area is y.
    . . Then: .xy = 704 . . y = 704/x [1]

    The length of the poster is x + 8.
    The height of the poster is y + 8.
    . . Then: .(x + 8)(y + 8) = 1200 [2]


    Substitute [1] into [2]: .(x + 8)(704/x + 8) .= .1200

    . . which simplifies to: .8x - 432x + 5632 .= .0

    . . Divide by 8: . x - 54x + 704 .= .0

    . . which factors: .(x - 22)(x - 32) .= .0

    . . and has roots: .x .= .22, 32 . . y .= .32, 22

    Hence, the dimensions of the printed area is: 22 x 32 inches.


    Therefore, the dimension of the poster is: 30 x 40 inches.

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