document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190223>Question 1190223</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a besieged fortress is held by 5700 men who have provisions for 66 days. of the garrison loses 20 men each day, for how many days will be provisions last? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #821844 by </B><A HREF=/tutors/aboutme.mpl?userid=Solver92311><B>Solver92311(821)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Solver92311><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=Solver92311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=821844\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Times New Roman\" size=\"+2\">\r<BR>\n" );
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document.write( "If 5700 men have rations for 66 days, then there must be a total of 5700 times 66 or 376200 rations available.\r<BR>\n" );
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document.write( "On the first day, 5700 rations are used, but on the second day, 20 less are used, and on the third day, 20 less than that.\r<BR>\n" );
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document.write( "The total rations used is given by:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=0}^n\,5700-20i\">\r<BR>\n" );
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document.write( "This is an arithmetic sequence where the first term is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5700\">, the common difference is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large -20\">, there are <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large n\ +\ 1\"> terms (zero start), and the last term is <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large 5700-20n\">.\r<BR>\n" );
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document.write( "Applying the formula for the sum of an arithmetic series:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ \sum_{i=0}^n\,5700-20i\ =\ (5700\,-\,10n)(n\,+\,1)\">\r<BR>\n" );
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document.write( "Set this equal to the known total rations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (5700\,-\,10n)(n\,+\,1)\ =\ 376200\">\r<BR>\n" );
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document.write( "And solve the quadratic for the smaller root\r<BR>\n" );
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document.write( "																<BR>\n" );
document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi}\ +\ 1\ =\ 0\"><BR>\n" );
document.write( "My calculator said it, I believe it, that settles it<BR>\n" );
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document.write( "From <https://www.algebra.com/cgi-bin/upload-illustration.mpl> <BR>\n" );
document.write( "I > Ø<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\Large \ \\r\"> </SPAN>\n" );
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