document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1163926>Question 1163926</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find a two digit number such that three times the tens digit is 2 less than<BR>\n" );
document.write( "twice the units digits and twice the number is 20 greater than the number<BR>\n" );
document.write( "obtained by reversing the digits </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #788262 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=788262\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Here is a very different method for solving the problem....<br><BR>\n" );
document.write( "Let t and u be the tens and units digits, respectively. Then we are told<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3t+=+2u-2 ALIGN=MIDDLE  ALT=\"3t+=+2u-2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Solve that single equation for t and use logical reasoning to find possible values for t and u, knowing that they are both positive single-digit integers.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%282u-2%29%2F3 ALIGN=MIDDLE  ALT=\"t+=+%282u-2%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%282%28u-1%29%29%2F3 ALIGN=MIDDLE  ALT=\"t+=+%282%28u-1%29%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since t has to be a positive integer, and since 2 is not divisible by 3, (u-1) must be positive and divisible by 3.<br><BR>\n" );
document.write( "That means there are only two possible values for u: 4 and 7.<br><BR>\n" );
document.write( "That in turn leads to only two possible values for the 2-digit number: 42 and 74.<br><BR>\n" );
document.write( "Only one of those satisfies the other condition of the problem.<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );