document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=387213>Question 387213</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a two digit number is 11 times its units digit. The sum of the digits is 12. find the number </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #276078 by </B><A HREF=/tutors/aboutme.mpl?userid=gwendolyn><B>gwendolyn(128)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gwendolyn><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=gwendolyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=276078\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let X be the tens digit<BR>\n" );
document.write( "Let Y be the units digit\r<BR>\n" );
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document.write( "The value of the two digit number is calculated as 10*X + Y, since X is the digit in the tens spot. Since this number is 11 times its units digit, then\r<BR>\n" );
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document.write( "10*X + Y = 11*Y<BR>\n" );
document.write( "Subtract Y from both sides:<BR>\n" );
document.write( "10*X + Y - Y = 11*Y - Y<BR>\n" );
document.write( "10*X = 10*Y<BR>\n" );
document.write( "Divide both sides by 10:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810%2AX%29%2F10+=+%2810%2AY%29%2F10 ALIGN=MIDDLE  ALT=\"%2810%2AX%29%2F10+=+%2810%2AY%29%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "X = Y<BR>\n" );
document.write( "(Which makes sense if you think about two-digit multiples of 11.)\r<BR>\n" );
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document.write( "The sum of the digits is 12, so:<BR>\n" );
document.write( "X + Y = 12\r<BR>\n" );
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document.write( "Substitute the value of X from the first equation:<BR>\n" );
document.write( "Y + Y = 12<BR>\n" );
document.write( "2*Y = 12<BR>\n" );
document.write( "Divide both sides by 2:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2AY%29%2F2+=+12%2F2 ALIGN=MIDDLE  ALT=\"%282%2AY%29%2F2+=+12%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Y = 6<BR>\n" );
document.write( "Substitute in the first equation for X:<BR>\n" );
document.write( "X = 6<BR>\n" );
document.write( "So, the two-digit number is 66 </SPAN>\n" );
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