document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1040539>Question 1040539</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular auditorium seats 2464 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #655362 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=655362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A rectangular auditorium seats 2464 people. The number of seats in each row exceeds the number of rows by 12. Find the number of seats in each row. <BR>\n" );
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document.write( "It is boring to solve a quadratic equation for this case.\r\n" );
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document.write( "I'd better calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282464%29 ALIGN=MIDDLE  ALT=\"sqrt%282464%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 49.6.\r\n" );
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document.write( "So, I think the answer is 56 and 44.\r\n" );
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document.write( "56*44 = 2464 !!!   Correct !!!\r\n" );
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document.write( "By the way, the quadratic equation is n*(n+12) = 2464,\r<BR>\n" );
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document.write( "and you can solve it on your own to find \"n\", the number of rows.\r<BR>\n" );
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document.write( "Hope you will get the answer n = 44.\r<BR>\n" );
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document.write( "There is one more way to solve the problem and to avoid boring calculations.\r\n" );
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document.write( "Let \"m\" be an unknown number which is 6 more than the number of rows: rows = m -6.\r\n" );
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document.write( "Then \"m\" is 6 less then the number of seats in a row: seats = m+6.\r\n" );
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document.write( "The product seats*rows = (m+6)*(m-6) = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2+-+36 ALIGN=MIDDLE  ALT=\"m%5E2+-+36\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2464.\r\n" );
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document.write( "Hence, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m%5E2 ALIGN=MIDDLE  ALT=\"m%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 2464 + 36 = 2500,  and  m = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%282500%29 ALIGN=MIDDLE  ALT=\"sqrt%282500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 50.\r\n" );
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document.write( "Then rows = m-6 = 50-6 = 44  and seats = m+6 = 50+6 = 56.\r\n" );
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document.write( "Solved.\r<BR>\n" );
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