document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=75181>Question 75181</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find digits a and b such that the number 34a47b5893 is divisible by 99. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #54005 by </B><A HREF=/tutors/aboutme.mpl?userid=nilan><B>nilan(17)</B></A><img src=\"/images/stars/stars-06.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nilan><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=54005\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Suppose 34a47b5893 is divisible by 99<BR>\n" );
document.write( "Then obviously it is divisible by 9<BR>\n" );
document.write( "If a number is divisible by 9 the sum of all the digits should divisible by 9 (this can be easily proved)\r<BR>\n" );
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document.write( "For example let the number abcd divisible by 9 then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%5E3a%2B10%5E2b%2B10c%2Bd+=+9k ALIGN=MIDDLE  ALT=\"10%5E3a%2B10%5E2b%2B10c%2Bd+=+9k\"   DISABLED_style= \"max-width:90%; height:auto;\" > where k is positive integer <BR>\n" );
document.write( "Then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1000a%2B100b%2B10c%2Bd+=+9k ALIGN=MIDDLE  ALT=\"1000a%2B100b%2B10c%2Bd+=+9k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28999a%2Ba%29%2B%2899b%2Bb%29%2B%289c%2Bc%29%2Bd=9k ALIGN=MIDDLE  ALT=\"%28999a%2Ba%29%2B%2899b%2Bb%29%2B%289c%2Bc%29%2Bd=9k\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc%2Bd+=+9k-%28999a%2B99b%2B9c%29 ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc%2Bd+=+9k-%28999a%2B99b%2B9c%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Bb%2Bc%2Bd+=+9%28k-111a%2B11b%2Bc%29=9K ALIGN=MIDDLE  ALT=\"a%2Bb%2Bc%2Bd+=+9%28k-111a%2B11b%2Bc%29=9K\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then a+b+d+c is divisible by 9<BR>\n" );
document.write( "This can be proved for any number (can be given a general proof. Try it)\r<BR>\n" );
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document.write( "Again to the problem <BR>\n" );
document.write( "Then the sum of 34a47b5893 is divisible by 9\r<BR>\n" );
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document.write( "Then 3+4+a+4+7+b+5+8+9+3 is divisible by 9<BR>\n" );
document.write( "Then<BR>\n" );
document.write( "43+a+b is divisible by nine \r<BR>\n" );
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document.write( "Then a=0 and b=2<BR>\n" );
document.write( "Or a=2 and b = 0  </SPAN>\n" );
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