document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1194635>Question 1194635</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A resort's enormous rectangular pool is 500 meters wide and 250 meters long. A contractor is<BR>\n" );
document.write( "hired to construct a brick walkway around the pool with an area of 1504 m^2?. What are the roots<BR>\n" );
document.write( "of the working equation? </SPAN>\n" );
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document.write( "Finding the width of the walkway (which SEEMS to be the objective) is much easier using common sense than with formal algebra.<br><BR>\n" );
document.write( "The sections of the walkway are two sections 500 by x meters, two sections 250 by x meters, and four section x by x meters.  With a total walkway area of 1504 meters, that gives us<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28500x%29%2B2%28250x%29%2B4x%5E2=1504 ALIGN=MIDDLE  ALT=\"2%28500x%29%2B2%28250x%29%2B4x%5E2=1504\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500x%2B4x%5E2=1504 ALIGN=MIDDLE  ALT=\"1500x%2B4x%5E2=1504\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Simple observation shows that x=1.<br><BR>\n" );
document.write( "But the problem doesn't ask us to find the width of the walkway; it asks us what the roots are of the \"working equation\".<br><BR>\n" );
document.write( "If we use the preceding discussion to form the \"working equation\", we have<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B1500x-1504=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B1500x-1504=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B375x-376=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B375x-376=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B376%29%28x-1%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B376%29%28x-1%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The roots are x=-376 and x=1<br><BR>\n" );
document.write( "A more standard way of setting up the problem leads to the same \"working equation\" by a different path.<br><BR>\n" );
document.write( "The area of the walkway is the area of (pool plus walkway), minus the area of the pool:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28500%2B2x%29%28250%2B2x%29-%28500%29%28250%29=1504 ALIGN=MIDDLE  ALT=\"%28500%2B2x%29%28250%2B2x%29-%28500%29%28250%29=1504\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28500%29%28250%29%2B1500x%2B4x%5E2-%28500%29%28250%29=1504 ALIGN=MIDDLE  ALT=\"%28500%29%28250%29%2B1500x%2B4x%5E2-%28500%29%28250%29=1504\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4x%5E2%2B1500x-1504=0 ALIGN=MIDDLE  ALT=\"4x%5E2%2B1500x-1504=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );