document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174393>Question 1174393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me with this word problem:\r<BR>\n" );
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document.write( "The length of a rectangular lot is 14 meters less than twice the lot’s width. The owner decided to decrease<BR>\n" );
document.write( "the length and the width by 3 meters each for landscaping purposes. The perimeter of the smaller<BR>\n" );
document.write( "rectangular lot is 80 meters. What is the area of the ORIGINAL lot in square meters? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #799915 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=799915\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let L = the length<BR>\n" );
document.write( "let W = the width.<BR>\n" );
document.write( "the perimeter of the lot is equal to 2 * (L + W)<BR>\n" );
document.write( "the area of the lot is equal to L * W\r<BR>\n" );
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document.write( "you are given that the length of a rectangular lot is 14 meters less than twice the lot’s width.\r<BR>\n" );
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document.write( "the equation for that is:<BR>\n" );
document.write( "L = 2W - 14\r<BR>\n" );
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document.write( "The owner decided to decrease the length and the width by 3 meters each for landscaping purposes. The perimeter of the smaller rectangular lot is 80 meters.\r<BR>\n" );
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document.write( "since perimeter = 2 * (L - 3 + W - 3), then your equation for this is:\r<BR>\n" );
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document.write( "80 = 2 * (L - 3 + W - 3)<BR>\n" );
document.write( "combine like terms in this to get:<BR>\n" );
document.write( "80 = 2 * (L + W - 6)<BR>\n" );
document.write( "simplify further to get:<BR>\n" );
document.write( "80 = 2L + 2W - 12\r<BR>\n" );
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document.write( "you were given that L = 2W - 14, therefore replace L with 2W - 14 in the equation of 80 = 2L + 2W - 12 to get:<BR>\n" );
document.write( "80 = 2 * (2W - 14) + 2W - 12<BR>\n" );
document.write( "simplify to get:<BR>\n" );
document.write( "80 = 4W - 28 + 2W - 12<BR>\n" );
document.write( "combine like terms to get:<BR>\n" );
document.write( "80 = 6W - 40<BR>\n" );
document.write( "add 40 to both sides of this equation to get:<BR>\n" );
document.write( "120 = 6W<BR>\n" );
document.write( "solve for W to get:<BR>\n" );
document.write( "W = 120 / 6 = 20\r<BR>\n" );
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document.write( "since L = 2W - 14, then L = 40 - 14 = 26\r<BR>\n" );
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document.write( "you have L = 26 and W = 20\r<BR>\n" );
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document.write( "taking 3 off of each, you have:<BR>\n" );
document.write( "L - 3 = 23<BR>\n" );
document.write( "W - 3 = 17\r<BR>\n" );
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document.write( "the formula for the perimeter becomes 80 = 2 * (23 + 17) = 46 + 34 = 80.<BR>\n" );
document.write( "this confirms the values for L and W are correct.\r<BR>\n" );
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document.write( "you want to know the area of the original lot.\r<BR>\n" );
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document.write( "that would be area = L * W = 26 * 20 = 520 square meters.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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