document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=382749>Question 382749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Each letter \"D\" \"N\" and \"A\" in this addition: DNA+DAN=AND ,represents a different digit. What is the sum of D + N + A?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #271172 by </B><A HREF=/tutors/aboutme.mpl?userid=richard1234><B>richard1234(7193)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=richard1234><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=richard1234><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=271172\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We have\r<BR>\n" );
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document.write( "(100D + 10N + A) + (100D + 10A + N) = 100A + 10N + D\r<BR>\n" );
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document.write( "200D + 11N + 11A = 100A + 10N + D\r<BR>\n" );
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document.write( "199D + N = 89A\r<BR>\n" );
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document.write( "Suppose we write the last expression modulo 89 to obtain\r<BR>\n" );
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document.write( "21D + N = 0 = 89 = 178 etc. (modulo 89)\r<BR>\n" );
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document.write( "21D + N cannot be 178 because D would become larger than 5 (which would give a 4-digit sum). Therefore 21D + N = 89 --> D = 4, N = 5.\r<BR>\n" );
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document.write( "Solving, we have\r<BR>\n" );
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document.write( "796 + 5 = 89A --> 801 = 89A --> A = 9\r<BR>\n" );
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document.write( "Therefore D + N + A = 18. </SPAN>\n" );
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