document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1179481>Question 1179481</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A theater can seat 247 people.  The number of rows is 6 less than the number of seats in each row.  How many rows of seats are there?\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 #809061 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=809061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The standard algebraic solution shown by the other tutor uses x and x+6 for the two numbers whose difference is 6; that leads to a solution in which you need to factor the quadratic equation<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B6x-247=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B6x-247=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "It will be difficult for most people to find that the correct factorization is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B19%29%28x-13%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B19%29%28x-13%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "leading to an answer of 13 rows of 19 seats each.<br><BR>\n" );
document.write( "Here is a technique that can be used to make an algebraic solution easier in this and many similar problems.<br><BR>\n" );
document.write( "Let the number of rows be x-3 and the number of seats in each row be x+3.<br><BR>\n" );
document.write( "Note the difference of 6 between the two numbers was implemented by letting x be halfway between the two numbers.<br><BR>\n" );
document.write( "Now the equation is solved much more easily:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-3%29%28x%2B3%29=247 ALIGN=MIDDLE  ALT=\"%28x-3%29%28x%2B3%29=247\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-9=247 ALIGN=MIDDLE  ALT=\"x%5E2-9=247\"   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=256 ALIGN=MIDDLE  ALT=\"x%5E2=256\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=16 ALIGN=MIDDLE  ALT=\"x=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The number of rows is x-3=13<br><BR>\n" );
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