document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=249487>Question 249487</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 60-Ft by 80-Ft parking lot is torn up to install a sidewalk of unirom width around it's perimeter. The new area of the parking lot is two-thirds of the old area. How wide is the sidewalk? Use the five step method to solve using algebra only. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #181741 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=181741\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the old parking lot is 60 feet by 80 feet.\r<BR>\n" );
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document.write( "let the length be 80 feet.\r<BR>\n" );
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document.write( "let the width be 60 feet.\r<BR>\n" );
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document.write( "the original area of the parking lot is 60 * 80 = 4800 square feet.\r<BR>\n" );
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document.write( "the new parking lot is going to be 2/3 * 4800 = 3200 square feet.\r<BR>\n" );
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document.write( "let x = the width of the sidewalk\r<BR>\n" );
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document.write( "this means that:\r<BR>\n" );
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document.write( "(60-x) * (80-x) = 3200\r<BR>\n" );
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document.write( "simplify by multiplying out the factors to get:\r<BR>\n" );
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document.write( "4800 - 60*x - 80*x + x^2 = 3200\r<BR>\n" );
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document.write( "simplify by combining like terms to get:\r<BR>\n" );
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document.write( "4800 - 140*x + x^2 = 3200\r<BR>\n" );
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document.write( "subtract 3200 from both sides of the equation to get:\r<BR>\n" );
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document.write( "4800 - 140*x + x^2 - 3200 = 0\r<BR>\n" );
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document.write( "simplify by combining like terms to get:\r<BR>\n" );
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document.write( "1600 - 140*x + x^2 = 0 which is the same as:\r<BR>\n" );
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document.write( "x^2 - 140*x + 1600 = 0\r<BR>\n" );
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document.write( "the standard form of a quadratic equation is:\r<BR>\n" );
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document.write( "ax^2 + bx + c = 0\r<BR>\n" );
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document.write( "in your equation:\r<BR>\n" );
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document.write( "a = 1<BR>\n" );
document.write( "b = -140<BR>\n" );
document.write( "c = 1600\r<BR>\n" );
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document.write( "use the quadratic formula to solve this since you can't find the factors easily by using the factor method.\r<BR>\n" );
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document.write( "the quadratic formula is:\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "x = 127.4456265 or x = 12.55437353\r<BR>\n" );
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document.write( "substitute in your original equation and you will see that both answers are valid solutions to the equation.\r<BR>\n" );
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document.write( "x = 127.4456265, however, is too large to be considered since it is greater than 80 or 60.\r<BR>\n" );
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document.write( "your answer has to be:\r<BR>\n" );
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document.write( "x = 12.55437353\r<BR>\n" );
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document.write( "the dimensions of the new parking lot will be:\r<BR>\n" );
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document.write( "60 - 12.55437353 = 47.44562647 feet.\r<BR>\n" );
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document.write( "80 - 12.55437353 = 67.44562647 feet.\r<BR>\n" );
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document.write( "47.44562647 * 67.44562647 = 3200 square feet.\r<BR>\n" );
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document.write( "the answers are confirmed as good.\r<BR>\n" );
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document.write( "the answer to your problem is:\r<BR>\n" );
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document.write( "the width of the sidewalk is 12.55437353 feet.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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