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Math Help - Word Problem Help

  1. #1
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    Jun 2009
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    Question Word Problem Help

    Got stuck on this one word problem that involves circles, rectangles and both their areas. I did not know where this would go so I put it here. I have a picture of the problem as an attachment also.

    Now about the problem. I had no trouble starting off with my picture and I defined my variables as:

    l-8= length of the yard(not border)
    w-8= width of the yard(not border)

    l= length of flower border
    w= width of flower border

    After that I wrote down my two equations:

    lw-667= 548 and (l-8)(w-8)= 1215

    I am stuck right now as I do not know what to do after simplifying both equations to:

    lw= 1215 and lw-8l-8w+64=1215

    Do I do substitution from here and then what? I do not want an answer I would be happy if someone could explain step by step what to do and how to get my solution for the two questions asked in the problem. This is as far as I got and the rest is confusing to me. Thank you in advance.
    Attached Thumbnails Attached Thumbnails Word Problem Help-problem3.gif  
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  2. #2
    MHF Contributor
    Joined
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    West Malaysia
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    Quote Originally Posted by gold4fools View Post
    Got stuck on this one word problem that involves circles, rectangles and both their areas. I did not know where this would go so I put it here. I have a picture of the problem as an attachment also.

    Now about the problem. I had no trouble starting off with my picture and I defined my variables as:

    l-8= length of the yard(not border)
    w-8= width of the yard(not border)

    l= length of flower border
    w= width of flower border

    After that I wrote down my two equations:

    lw-667= 548 and (l-8)(w-8)= 1215

    I am stuck right now as I do not know what to do after simplifying both equations to:

    lw= 1215 and lw-8l-8w+64=1215

    Do I do substitution from here and then what? I do not want an answer I would be happy if someone could explain step by step what to do and how to get my solution for the two questions asked in the problem. This is as far as I got and the rest is confusing to me. Thank you in advance.

    You are given 2 equations here :

    wl=1215 ---1

     wl-8l-8w+64=1215 ---2

    From 1 , we can write it this way : w=\frac{1215}{l}

    Then substitute into 2 , giving

     <br />
\frac{1215}{l}-8l-8\frac{1215}{l}+64=1215<br />

    1215-8l^2-9720+64l=1215l

     <br />
-8505-8l^2-1151l=0 <br />

    Can you solve this quadratic equation for l , then look for w .

    Is this what u want to know ?
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  3. #3
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by gold4fools View Post
    Got stuck on this one word problem that involves circles, rectangles and both their areas. I did not know where this would go so I put it here. I have a picture of the problem as an attachment also.

    Now about the problem. I had no trouble starting off with my picture and I defined my variables as:

    l-8= length of the yard(not border)
    w-8= width of the yard(not border)

    l= length of flower border
    w= width of flower border

    After that I wrote down my two equations:

    lw-667= 548 and (l-8)(w-8)= 1215

    I am stuck right now as I do not know what to do after simplifying both equations to:

    lw= 1215 and lw-8l-8w+64=1215

    Do I do substitution from here and then what? I do not want an answer I would be happy if someone could explain step by step what to do and how to get my solution for the two questions asked in the problem. This is as far as I got and the rest is confusing to me. Thank you in advance.
    lw=667 and (l+8)(w+8)-667=548

    Solve for l or w in one of these equations

    (l+8)(w+8)-667=548
    (l+8)(w+8)=1215
    l=\frac{1215}{w+8}-8

    now substitute
    [\frac{1215}{w+8}-8]w=667

    the rest is easy. just make the radius of your circle as long as half of the diagonal of the rectangle, find the area, and then subtract 1215 grom that area to find the wasted water.
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