document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1045027>Question 1045027</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Two different numbers when divided by the same divisor, left remainders 11 & 21 respectively.When their sum was divided by the same divisor , remainder was 4.What is the divisor ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #660455 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=660455\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28EDITED%29 ALIGN=MIDDLE  ALT=\"red%28EDITED%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28SOLUTION%29 ALIGN=MIDDLE  ALT=\"red%28SOLUTION%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (Sorry about the typo):<BR>\n" );
document.write( "We are told that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number%5B1%5D=divisor%2Aquotient%5B1%5D%2B11 ALIGN=MIDDLE  ALT=\"number%5B1%5D=divisor%2Aquotient%5B1%5D%2B11\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number%5B2%5D=divisor%2Aquotient%5B2%5D%2B21 ALIGN=MIDDLE  ALT=\"number%5B2%5D=divisor%2Aquotient%5B2%5D%2B21\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, adding up those two equations, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number%5B1%5D%2Bnumber%5B2%5D=divisor%2Aquotient%5B1%5D%2Bdivisor%2Aquotient%5B2%5D%2B11%2B21 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number%5B1%5D%2Bnumber%5B2%5D=divisor%2A%28quotient%5B1%5D%2Bquotient%5B2%5D%29%2B32 ALIGN=MIDDLE  ALT=\"number%5B1%5D%2Bnumber%5B2%5D=divisor%2A%28quotient%5B1%5D%2Bquotient%5B2%5D%29%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Since we are also told that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number%5B1%5D%2Bnumber%5B2%5D=divisor%2Aquotient%5B3%5D%2B4 ALIGN=MIDDLE  ALT=\"number%5B1%5D%2Bnumber%5B2%5D=divisor%2Aquotient%5B3%5D%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "subtracting from the equation above from<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=number%5B1%5D%2Bnumber%5B2%5D=divisor%2A%28quotient%5B1%5D%2Bquotient%5B2%5D%29%2B32 ALIGN=MIDDLE  ALT=\"number%5B1%5D%2Bnumber%5B2%5D=divisor%2A%28quotient%5B1%5D%2Bquotient%5B2%5D%29%2B32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=divisor%2A%28quotient%5B3%5D-quotient%5B1%5D-quotient%5B2%5D%29%2B4-32 ALIGN=MIDDLE  ALT=\"0=divisor%2A%28quotient%5B3%5D-quotient%5B1%5D-quotient%5B2%5D%29%2B4-32\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=divisor%2A%28quotient%5B3%5D-quotient%5B1%5D-quotient%5B2%5D%29-28 ALIGN=MIDDLE  ALT=\"0=divisor%2A%28quotient%5B3%5D-quotient%5B1%5D-quotient%5B2%5D%29-28\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28=divisor%2A%28quotient%5B3%5D-quotient%5B1%5D-quotient%5B2%5D%29 ALIGN=MIDDLE  ALT=\"28=divisor%2A%28quotient%5B3%5D-quotient%5B1%5D-quotient%5B2%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since all the numbers involved in that equation are integers,<BR>\n" );
document.write( "that tells us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=divisor ALIGN=MIDDLE  ALT=\"divisor\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and it has to be a factor larger than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28cross%2828%29%29 ALIGN=MIDDLE  ALT=\"red%28cross%2828%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" > was a remainder,<BR>\n" );
document.write( "and remainders are always smaller than their divisor.<BR>\n" );
document.write( "The only factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" > that is greater than <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=28 ALIGN=MIDDLE  ALT=\"28\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2828%29 ALIGN=MIDDLE  ALT=\"highlight%2828%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the divisor.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );