document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=698987>Question 698987</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a number of 3 digits is such hat the tens digit exceeds the unit digit by 2. If this number exceeds the number formed by reversing the digits 297 ad if the sum of its digits is 14, 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 #431171 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=431171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a number of 3 digits is such hat the tens digit exceeds the unit digit by 2.<BR>\n" );
document.write( " If this number exceeds the number formed by reversing the digits by 297 <BR>\n" );
document.write( "and if the sum of its digits is 14, find the number.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let a = the 100's digit<BR>\n" );
document.write( "Let b = the 10's digit<BR>\n" );
document.write( "Let c = the units<BR>\n" );
document.write( "then<BR>\n" );
document.write( "100a + 10b + c = \"the 3digit number<BR>\n" );
document.write( "and<BR>\n" );
document.write( "100c + 10b + a = the number reversed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" the tens digit exceeds the unit digit by 2.\"<BR>\n" );
document.write( "b = c+2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" If this number exceeds the number formed, by reversing the digits by 297\"<BR>\n" );
document.write( "100a + 10b + c = 100c + 10b + a + 297<BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "100a - a + 10b - 10b = 100c - c + 297<BR>\n" );
document.write( "99a = 99c + 297<BR>\n" );
document.write( "Simplify, divide by 99<BR>\n" );
document.write( "a = c + 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"the sum of its digits is 14,\"<BR>\n" );
document.write( "a + b + c = 14<BR>\n" );
document.write( "replace a with (c+3), replace b with (c+2)<BR>\n" );
document.write( "c + 3 + c + 2 + c = 14<BR>\n" );
document.write( "3c + 5 = 14<BR>\n" );
document.write( "3c = 14 - 5<BR>\n" );
document.write( "c = 9/3<BR>\n" );
document.write( "c = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "I'll let you find a and b<BR>\n" );
document.write( "check the number you come up with in each statement<BR>\n" );
document.write( " <BR>\n" );
document.write( ":<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );