document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1174157>Question 1174157</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Mary uses a secret code to write messages. First she translates each letter of the alphabet into a number based on its position in the alphabet, so that A = 1, B = 2, C = 3, and so on. Then she multiplies this number by her favorite number and adds her mother's favorite number. Using her secret code, F becomes 41 and T becomes 83.\r<BR>\n" );
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document.write( "Find what number M becomes.\r<BR>\n" );
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document.write( "What are Mary's favorite number and her mother's favorite number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #799557 by </B><A HREF=/tutors/aboutme.mpl?userid=htmentor><B>htmentor(1343)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=htmentor><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=htmentor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=799557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = Mary's favorite number<BR>\n" );
document.write( "Let y = Mom's favorite number<BR>\n" );
document.write( "The general formula for the encoded number is x*n + y, where n is the number's<BR>\n" );
document.write( "position in the alphabet<BR>\n" );
document.write( "41 = 6x + y<BR>\n" );
document.write( "83 = 20x + y<BR>\n" );
document.write( "Subtract the 1st from the 2nd:<BR>\n" );
document.write( "42 = 14x -> x = 3<BR>\n" );
document.write( "Thus y = 41 - 6*3 = 23<BR>\n" );
document.write( "Therefore M = 13*3 + 23 = 62\r<BR>\n" );
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