document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=466398>Question 466398</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I was doing an IQ game (\"challenging\" level) and was faced with a problem, which I solved by logical thinking and trial/error. However, before that I tried to figure out a way to solve the problem with algebra. I'm still not sure if it is possible or not.\r<BR>\n" );
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document.write( "The problem/question:<BR>\n" );
document.write( "\"Charlie removed a one-metre wide strip of grass from all the way around a square lawn, which was made info a flower bed. The remaining grass was four-fifths the area of the new flower bed.<BR>\n" );
document.write( "What were the dimensions of the lawn originally?\"\r<BR>\n" );
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document.write( "It seemed to me that we are missing a value (a length), but then I thought that it might be possible to figure it out by using equations, and canceling out values against each other. I tried different approaches, but I haven't done equations for a long time and got stuck.\r<BR>\n" );
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document.write( "This was my approach:<BR>\n" );
document.write( "a = length or height of square lawn<BR>\n" );
document.write( "b = new flower bed<BR>\n" );
document.write( "c = remaining grass<BR>\n" );
document.write( "d = dimensions of original lawn (area)\r<BR>\n" );
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document.write( "c = 4/5b<BR>\n" );
document.write( "d = b + c<BR>\n" );
document.write( "(a - 2)x2 = (4/5b) + (5/5b)\r<BR>\n" );
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document.write( "Is it just not possible, or am I missing something? <BR>\n" );
document.write( "Any help with pointing out if and how this can be done would be greatly appreciated!\r<BR>\n" );
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document.write( "Kind regards,<BR>\n" );
document.write( "Rob </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #319744 by </B><A HREF=/tutors/aboutme.mpl?userid=scott8148><B>scott8148(6628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=scott8148><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=scott8148><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=319744\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the original square lawn had a side length of S, then the remaining grass square had a side length of S-2 (one meter removed from each end)\r<BR>\n" );
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document.write( "the new grass square is 4/5 the area of the one meter border (flower bed), whose area is 5/5 of itself<BR>\n" );
document.write( "___ this means that the grass is 4/9 (4 / [4+5]) of the total area\r<BR>\n" );
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document.write( "(4/9)S^2 = (S - 2)^2 ___ 4S^2 = 9S^2 - 36 S + 36 ___ 0 = 5S^2 - 36 S + 36\r<BR>\n" );
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document.write( "factoring ___ (5S - 6)(S - 6) = 0\r<BR>\n" );
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document.write( "5S - 6 = 0 ___ S = 6/5 ___ not realistic considering the one meter border reduction\r<BR>\n" );
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document.write( "S - 6 = 0 ___ S = 6 </SPAN>\n" );
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