document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=198520>Question 198520</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular flower bed 30 yards long by 20 yards wide has a walk of uniform width around it. If the area of the path is 1/4 that of the flower bed, find the width of the path. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #149044 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=149044\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">     A rectangular flower bed 30 yards long by 20 yards wide has a walk of uniform width around it. If the area of the path is 1/4 that of the flower bed, find the width of the path.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let w = width of path<BR>\n" );
document.write( "then<BR>\n" );
document.write( "Area of flower bed = (30)(20) = 600 sq yards<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Area of flower bed and walk = (30+2w)(20+2w)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Area of path = \"area of flower bed and walk\" - \"area of flower bed\"<BR>\n" );
document.write( "Area of path = (30+2w)(20+2w) - 600<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(1/4)600 = (30+2w)(20+2w) - 600<BR>\n" );
document.write( "150 = (30+2w)(20+2w) - 600<BR>\n" );
document.write( "750 = (30+2w)(20+2w)<BR>\n" );
document.write( "750 = 600+60w+40w+4w^2<BR>\n" );
document.write( "750 = 4w^2+100w+600<BR>\n" );
document.write( "0 = 4w^2+100w-150<BR>\n" );
document.write( "0 = 2w^2+50w-75<BR>\n" );
document.write( "Using the quadratic equation we get:<BR>\n" );
document.write( "w = {1.42, -26.42}<BR>\n" );
document.write( "Throw out the negative solution leaves us with:<BR>\n" );
document.write( "w = 1.42 yards<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic to follow:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aw%5E2%2Bbw%2Bc=0 ALIGN=MIDDLE  ALT=\"aw%5E2%2Bbw%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2B50w%2B-75+=+0 ALIGN=MIDDLE  ALT=\"2w%5E2%2B50w%2B-75+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"w%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%2850%29%5E2-4%2A2%2A-75=3100 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%2850%29%5E2-4%2A2%2A-75=3100\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=3100 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-50%2B-sqrt%28+3100+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-50%2B-sqrt%28+3100+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B1%5D+=+%28-%2850%29%2Bsqrt%28+3100+%29%29%2F2%5C2+=+1.41941090707505 ALIGN=MIDDLE  ALT=\"w%5B1%5D+=+%28-%2850%29%2Bsqrt%28+3100+%29%29%2F2%5C2+=+1.41941090707505\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=w%5B2%5D+=+%28-%2850%29-sqrt%28+3100+%29%29%2F2%5C2+=+-26.4194109070751 ALIGN=MIDDLE  ALT=\"w%5B2%5D+=+%28-%2850%29-sqrt%28+3100+%29%29%2F2%5C2+=+-26.4194109070751\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2B50w%2B-75 ALIGN=MIDDLE  ALT=\"2w%5E2%2B50w%2B-75\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2w%5E2%2B50w%2B-75+=+2%28w-1.41941090707505%29%2A%28w--26.4194109070751%29 ALIGN=MIDDLE  ALT=\"2w%5E2%2B50w%2B-75+=+2%28w-1.41941090707505%29%2A%28w--26.4194109070751%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 1.41941090707505, -26.4194109070751.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B50%2Ax%2B-75+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+2%2Ax%5E2%2B50%2Ax%2B-75+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );