document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1055383>Question 1055383</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Determine the largest integer less than or equal to 2016 that leaves a remainder of 3 when divided by 7 and leaves a remainder of 4 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 #670649 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=670649\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> it looks like the number will be 1984.\r<BR>\n" );
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document.write( "i don't know if there's an easy way to do this.\r<BR>\n" );
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document.write( "this is how i did it.\r<BR>\n" );
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document.write( "divide 2016 by 7 and you get 288 with a remainder of 0.<BR>\n" );
document.write( "subtract 4 from 2016 and you get 2012.<BR>\n" );
document.write( "divide 2012 by 7 and you get 287 with a remainder of 3.<BR>\n" );
document.write( "that's the largest number less than or equal to 2016 that is divisible by 7 with a remainder of 3.\r<BR>\n" );
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document.write( "divide 2016 by 11 and you get 183 with a remainder of 3.<BR>\n" );
document.write( "add 1 to 2016 and you get 2017.<BR>\n" );
document.write( "divide 2017 by 11 and you get 183 with a remainder of 4.<BR>\n" );
document.write( "you got the remainder of 4 but 2017 is greater than 2016, so that's no good.<BR>\n" );
document.write( "subtract 11 from 2017 and you get 2006.<BR>\n" );
document.write( "divide 20006 by 11 and you get 182 with a remainder of 4.<BR>\n" );
document.write( "that's the largest number less than or equal to 2016 that is divisible by 11 with a remainder of 4.\r<BR>\n" );
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document.write( "your two largest numbers are:\r<BR>\n" );
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document.write( "2012 and 2006.\r<BR>\n" );
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document.write( "you want to find the largest number that is divisible by both and leaves a remainder of 3 when divided by 7 and leaves a remainder of 4 when divided by 11.\r<BR>\n" );
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document.write( "work your way down each set.\r<BR>\n" );
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document.write( "2012 is reduced by 7 each time.<BR>\n" );
document.write( "2006 is reduced by 11 each time.\r<BR>\n" );
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document.write( "you get:\r<BR>\n" );
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document.write( "2012 - 7 = 2005 - 7 = 1998 - 7 = 1991 - 7 = 1984\r<BR>\n" );
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document.write( "2006 - 11 = 1995 - 11 = 1984.\r<BR>\n" );
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document.write( "1984 is the magic number as best i can determine.\r<BR>\n" );
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document.write( "when it is divided by 7, you get 283 plus a remainder of 3.<BR>\n" );
document.write( "when it is divided by 11, you get 180 plus a remainder of 4.\r<BR>\n" );
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document.write( "there may be an easier way to figure this out but i don't know it.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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