document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=257183>Question 257183</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this word problem:   The sum of the digits of a two-digit number is 12.  The number is 12 times the tens digit.  Find the number.  I need to know how you got the equations please. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #189118 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=189118\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = the tens digit.<BR>\n" );
document.write( "let b = the ones digit.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a + b = 12 (sum of the digits is equal to 12).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "10a + b = 12*a (the number is 12 times the tens digit).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve for a in the first equation to get a = 12-b.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "substitute for a in the second equation to get 10*(12-b) + b = 12*(12-b).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "simplify to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "120 - 10b + b = 144 - 12b.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "combine like terms to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "120 - 9b = 144 - 12b.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "add 12b to both sides of the equation and subtract 120 from both sides of the equation to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "3b = 24\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "divide both sides of the equation by 3 to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "b = 8\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if b = 8, then a = 4 because a + b = 8 + 4 = 12.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the number is 10*a + b = 40 + 8 = 48\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "48 is equal to 12*a = 12*4 = 48 so that part of the equation is good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "a + b = 4 + 8 = 12 so that part of the equation is also good.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "your answer is the number is 48.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );