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Math Help - Find the width of a frame

  1. #1
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    Find the width of a frame

    The printed matter on a 12 by 24 centimeter page of a book must cover 64 square centimeters. If all margins are to be the same width, how wide should the margins be?
    Last edited by cechmanek32; June 25th 2008 at 11:38 AM. Reason: I posted the wrong one...sorry!
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    Quote Originally Posted by cechmanek32 View Post
    Somebody please help me...I really have no idea what to do. I'm not even sure where to start! Here is my problem, and if someone could show me the steps I Would REALLY appreciate it! Thanks is advance!

    The length of a rectangular frame is 5 cm more than the width. The area inside the frame is 84 square cm. Find the width of the frame.
    So we need a few formulas to start.

    The area of a rectangle is A=L \cdot W

    We know the area A=84 in^2

    We also know that the length is five more than the width so

    L=W+5 and that the width is W.

    Now we evaluate the area formula to get

    84=(W+5)W \iff 84=W^2+5W \iff 0=W^2+5W-84
     0= (W+12)(W-7)

    So now using the zero product priciple we set each factor equal to zero to get

    W+12=0 \iff W=-12 and W-7=0 \iff W=7

    Since we are talking about the width of a frame the negative solution doesn't make sense so we are left with the width of the frame is 7 in.

    Good luck.
    Last edited by TheEmptySet; June 25th 2008 at 11:47 AM. Reason: La Tex error
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    Quote Originally Posted by cechmanek32 View Post
    The printed matter on a 12 by 24 centimeter page of a book must cover 64 square centimeters. If all margins are to be the same width, how wide should the margins be?
    Let x be the size of the margins. Then the length of the printed matter is 24-2x and the width is 12-2x

    Using the Area formula from the above post we get

    64=(24-2x)(12-2x) we can factor a 2 out of each factor on the left hand side to get

    64=2\cdot 2\cdot (12-x)(6-x) now we can reduce the equation by dividing both sides by 4 to get

    16=(12-x)(6-x) Now we expand the right hand side to get

    16=72-18x+x^2 \iff x^2-18x+56=0 \iff (x-14)(x-4)=0

    So we get that x=14 or x=4

    We reject the first solution becuase if we plug it back into the original equation the length and width are negative so x =4 is the solution.

    The margins should be 4cm
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  4. #4
    Moo
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    Hello,

    Quote Originally Posted by cechmanek32 View Post
    The printed matter on a 12 by 24 centimeter page of a book must cover 64 square centimeters. If all margins are to be the same width, how wide should the margins be?
    Find the width of a frame-printed.jpg


    Edit : uuum, too late
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  5. #5
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    Quote Originally Posted by Moo View Post
    Hello,



    Click image for larger version. 

Name:	printed.JPG 
Views:	33 
Size:	20.5 KB 
ID:	6970


    Edit : uuum, too late
    But, you added another element....a diagram. Diagrams are cool. Like driving in a red convertible.
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