document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1022958>Question 1022958</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three times the tens digit of a certain 2 digit number is 2 more than four times the units digit. The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits. Find the number?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #638521 by </B><A HREF=/tutors/aboutme.mpl?userid=addingup><B>addingup(3677)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=addingup><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=addingup><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=638521\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let's call the number xy. Since x is the tens digit:<BR>\n" );
document.write( "10x+y<BR>\n" );
document.write( "The problem says:<BR>\n" );
document.write( "3x = 4y+2 Subtract 4y from both sides:<BR>\n" );
document.write( "3x-4y = 2<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "The difference between the given number and the number obtained by reversing the digits is two less than twice the sum of the digits:<BR>\n" );
document.write( "10x+y-10y-x = 2(x+y)-2 Subtract on left and multiply on right:<BR>\n" );
document.write( "9x-9y = 2x+2y-2 Subtract 2x and 2y on both sides:<BR>\n" );
document.write( "7x-11y = -2<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "Now we have two equations:<BR>\n" );
document.write( "3x-4y = 2 (Multiply both sides of this equation times -7)<BR>\n" );
document.write( "and<BR>\n" );
document.write( "7x-11y = -2 (Multiply both sides of this equation times 3)<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~<BR>\n" );
document.write( "-21x+28y = -14<BR>\n" );
document.write( "+<BR>\n" );
document.write( "21x-33y = -6<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( ". . -5y = -20 <BR>\n" );
document.write( "Divide both sides by -5<BR>\n" );
document.write( "y = 4<BR>\n" );
document.write( "Now that we know y let's find x. The problem says:<BR>\n" );
document.write( "3x = 4y+2 substitute for y:<BR>\n" );
document.write( "3x = 4(4)+2<BR>\n" );
document.write( "3x = 16+2 Add on right and divide both sides by 3<BR>\n" );
document.write( "x = 6<BR>\n" );
document.write( "So, your tens digit is 6 and 6*10 = 60 and you singles digit is 4, and 60+4 = 64. This is your number: 64 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );