document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=71783>Question 71783</A>: <I><SPAN STYLE=\"word-break: break-all;\"> H E L P !!!!!! How do you solve:\r<BR>\n" );
document.write( "\n" );
document.write( "A three-digit number is 198 more than the number formed by reversing the digits.  The 100's digit is 3 more than the 10's digit.  The sum of the digits is 16.  What is the original number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #51509 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=51509\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A three-digit number is 198 more than the number formed by reversing the digits.<BR>\n" );
document.write( " The 100's digit is 3 more than the 10's digit. The sum of the digits is 16. What<BR>\n" );
document.write( " is the original number?<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Let x = 100's digit of original number<BR>\n" );
document.write( "Let y = 10's digit<BR>\n" );
document.write( "Let z = 1's digit of original number:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Original number - Reversed number = 198<BR>\n" );
document.write( "(100x + 10y + z) - (100z + 10y + x) = 198<BR>\n" );
document.write( ":<BR>\n" );
document.write( "100x + 10y + z - 100z - 10y - x = 198<BR>\n" );
document.write( ":<BR>\n" );
document.write( "99x - 99z = 198<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Simplify, divide by 99<BR>\n" );
document.write( "x - z = 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"The 100's digit is 3 more than the 10's digit.\" <BR>\n" );
document.write( "x = y + 3<BR>\n" );
document.write( "x - y = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"The sum of the digits is 16\"<BR>\n" );
document.write( "x + y + z = 16<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Three equations:<BR>\n" );
document.write( "x + 0y - 1z = 2<BR>\n" );
document.write( "x - 1y + 0z = 3<BR>\n" );
document.write( "x + 1y + 1z = 16<BR>\n" );
document.write( "------------------ adding eliminates y and z<BR>\n" );
document.write( "3x +0y + 0z = 21<BR>\n" );
document.write( "3x = 21<BR>\n" );
document.write( "x = 21/3<BR>\n" );
document.write( "x = 7<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find z using; x - z = 2<BR>\n" );
document.write( "7 - z = 2<BR>\n" );
document.write( "z = 5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find y using: x - y = 3<BR>\n" );
document.write( "7 - y = 3<BR>\n" );
document.write( "y = 4<BR>\n" );
document.write( ":<BR>\n" );
document.write( "our number is 745<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check: 745 - 547 = 198\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "	 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );