document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=29162>Question 29162</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,i'm using factoring to solve problems,and I can't figure this out. Here's the question: A rectangular garden 30 meters by 40 meters has two paths of equal width crossing through it.Find the width of each path if the total area covered by the paths is 325m^2.Thanks a lot!                                   \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #15951 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=15951\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the width of the paths be x meters.<BR>\n" );
document.write( "The combined area of the two paths can be written:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40x+%2B+30x+-+x%5E2+=+325 ALIGN=MIDDLE  ALT=\"40x+%2B+30x+-+x%5E2+=+325\"   DISABLED_style= \"max-width:90%; height:auto;\" > The subtraction of<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > takes into account the overlapping area of the paths' intersection which would otherwise be counted twice. So now you need to solve the quadratic equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-70x+%2B+325+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-70x+%2B+325+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factor.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-65%29%28x-5%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-65%29%28x-5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the zero products principle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-65%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-65%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and/or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29+=+0 ALIGN=MIDDLE  ALT=\"%28x-5%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-65+=+0 ALIGN=MIDDLE  ALT=\"x-65+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+65 ALIGN=MIDDLE  ALT=\"x+=+65\"   DISABLED_style= \"max-width:90%; height:auto;\" > Discard this solution as the path can't be wider than the garden.<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5+=+0 ALIGN=MIDDLE  ALT=\"x-5+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5 ALIGN=MIDDLE  ALT=\"x+=+5\"   DISABLED_style= \"max-width:90%; height:auto;\" > This solution is valid.<BR>\n" );
document.write( "The width of the path is 5 meters.<BR>\n" );
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