document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=818108>Question 818108</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular auditorium seats 1505 people. The number of seats in each row exceeds the number of rows by 8. 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 #729123 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</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=729123\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "I definitely concur with tutor ikleyn that this kind of problem is much better solved using a little logical reasoning, instead of formal mathematics.  Indeed, when you try to solve it using the traditional algebraic approach, you end up having to factor a quadratic by finding two numbers whose product is 1505 and whose difference is 8.  But THAT IS WHAT THE ORIGINAL PROBLEM asks you to do.<br><BR>\n" );
document.write( "So the formal algebra is a waste of time....<br><BR>\n" );
document.write( "And the \"trick\" tutor ikleyn uses is a very useful one.  If you know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%28x-8%29=1505 ALIGN=MIDDLE  ALT=\"x%28x-8%29=1505\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then you know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B4%29%28x-4%29+=+1505%2B4%5E2+=+1505%2B16+=+1521+=+39%5E2 ALIGN=MIDDLE  ALT=\"%28x%2B4%29%28x-4%29+=+1505%2B4%5E2+=+1505%2B16+=+1521+=+39%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and so the answers are 39-4=35 and 39+4=43.<br><BR>\n" );
document.write( "It did not occur to me to use that trick on this problem.  I just started playing with numbers to find a pair with a product of 1505 and a difference of 8.  There weren't many possibilities....<br><BR>\n" );
document.write( "I of course first saw<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1505+=+5%2A301 ALIGN=MIDDLE  ALT=\"1505+=+5%2A301\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Then I had to find a factorization of 301; when I found it, I had my answer.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=301+=+7%2A43 ALIGN=MIDDLE  ALT=\"301+=+7%2A43\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1505+=+5%2A7%2A43+=+35%2A43 ALIGN=MIDDLE  ALT=\"1505+=+5%2A7%2A43+=+35%2A43\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "Answer: 35 rows of 43 seats each. </SPAN>\n" );
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