document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=993570>Question 993570</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What are five sequential numbers whose total is 63 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #612810 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52790)</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=612810\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "It is about this problem again and again:\r<BR>\n" );
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document.write( "Mr. &nbsp;<B>X</B>&nbsp; had a habit of spending money according to dates. &nbsp;For example, &nbsp;if date was &nbsp;19&nbsp; he was spending &nbsp;19 rupees, &nbsp;and if date was &nbsp;15&nbsp; he was spending &nbsp;15 rupees. <BR>\n" );
document.write( "One night he calculated total spending of &nbsp;5&nbsp; consecutive days - Monday to Friday, &nbsp;and he found that he spent &nbsp;63 rupees in &nbsp;5&nbsp; days. <BR>\n" );
document.write( "So, &nbsp;identify the dates. &nbsp;(Assume that everyday spending is integer number of rupees). <BR>\n" );
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document.write( "<B>Answer</B>. &nbsp;There is only one solution:\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;28 and 29 &nbsp;of February of a leap-year and &nbsp;1, 2, &nbsp;and &nbsp;3 &nbsp;of March.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(28 + 29 + 1 + 2 + 3 = 63). \r<BR>\n" );
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document.write( "<B>Solution</B>\r<BR>\n" );
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document.write( "If these days would be inside one month, &nbsp;then the dates are &nbsp;(x-2), &nbsp;(x-1), &nbsp;x, &nbsp;(x+1) &nbsp;and &nbsp;(x+2), &nbsp;where x is the date in the middle of &nbsp;5 days. \r<BR>\n" );
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document.write( "Then the sum must be multiple of &nbsp;5, &nbsp;since \r<BR>\n" );
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document.write( "(x-2) + (x-1) + x + (x+1) + (x+2) = 5x.\r<BR>\n" );
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document.write( "But the integer &nbsp;63&nbsp; is not multiple of &nbsp;5. &nbsp;Contradiction. \r<BR>\n" );
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document.write( "Hence, &nbsp;the dates are partly the end of some month and the beginning of the next month. \r<BR>\n" );
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document.write( "Then, &nbsp;it is easy to check that the dates &nbsp;28, &nbsp;29, &nbsp;1, &nbsp;2 &nbsp;and 3 &nbsp;satisfy the condition &nbsp;28 + 29 + 1 + 2 + 3 = 63. \r<BR>\n" );
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document.write( "Next, &nbsp;it is easy to check that there is no other solution.\r<BR>\n" );
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document.write( "The solution of this problem was placed in this forum one week ago <BR>\n" );
document.write( "http://www.algebra.com/algebra/homework/word/misc/Miscellaneous_Word_Problems.faq.question.992162.html .\r<BR>\n" );
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document.write( "The solution for the similar problem was placed in the lesson &nbsp;<A  rel=nofollow HREF=http://www.algebra.com/algebra/homework/word/misc/Spending-money-according-to-dates.lesson>Spending money according to dates</A>&nbsp; in this site couple of weeks ago.\r<BR>\n" );
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