document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=241175>Question 241175</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Reconciling remainders. Find a positive integer smaller<BR>\n" );
document.write( "than 500 that has a remainder of 3 when divided by 5, a<BR>\n" );
document.write( "remainder of 6 when divided by 9, and a remainder of 8<BR>\n" );
document.write( "when divided by 11. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #176662 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=176662\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Reconciling remainders. <BR>\n" );
document.write( "Find a positive integer smaller than 500 that has a remainder of 3 when divided by 5,<BR>\n" );
document.write( " a remainder of 6 when divided by 9, and a remainder of 8 when divided by 11.<BR>\n" );
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document.write( "we know <BR>\n" );
document.write( "x = multiple of 5 + 3, last digit is either 3 or 8<BR>\n" );
document.write( "x = multiple of 9 + 6<BR>\n" );
document.write( "x = multiple of 11 + 8,<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find a multiple of 11 + 8, last digit is 3 or 8<BR>\n" );
document.write( "then test to see if it is a multiple of 9 with a remainder 6<BR>\n" );
document.write( ":<BR>\n" );
document.write( "working downward from 500, I came up with 393<BR>\n" );
document.write( "(I used the table on the TI83, with the equation y = 11x + 8, look for last digit of 3 or 8)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "393/5 = 78 r3<BR>\n" );
document.write( "393/9 = 43 r6<BR>\n" );
document.write( "393/11= 35 r8<BR>\n" );
document.write( ":<BR>\n" );
document.write( "There is probably a neater way of doing this but I can't come up with it<BR>\n" );
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