document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891368>Question 891368</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the first and third digits of a 3 digit number are interchanged, the difference between the original number and the new one is 198. If the first and second digits of the original are interchanged the new one is 90 less than the original. The difference bewtween the first and third digits is equal to the second digit. Find 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 #539691 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=539691\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = the 100's digit<BR>\n" );
document.write( "let b = the 10's<BR>\n" );
document.write( "let c = the units<BR>\n" );
document.write( "then<BR>\n" );
document.write( "100a+10b+c = the original number<BR>\n" );
document.write( ":<BR>\n" );
document.write( "write an equation for each equation, simplify as much as possible.<BR>\n" );
document.write( ":<BR>\n" );
document.write( "if the first and third digits of a 3 digit number are interchanged, the difference between the original number and the new one is 198.<BR>\n" );
document.write( "100a + 10b + c - (100c + 10b +a) = 198<BR>\n" );
document.write( "removing the brackets changes the signs<BR>\n" );
document.write( "100a + 10b + c - 100c - 10b - a = 198<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "100a - a + 10b - 10b + c - 100c = 198<BR>\n" );
document.write( "99a - 99c = 198<BR>\n" );
document.write( "simplify, divide by 99<BR>\n" );
document.write( "a - c = 2<BR>\n" );
document.write( "c = a - 2; use for substitution<BR>\n" );
document.write( ":<BR>\n" );
document.write( " If the first and second digits of the original are interchanged the new one is 90 less than the original<BR>\n" );
document.write( "100a + 10b + c - (100b + 10a + c) = 90<BR>\n" );
document.write( "do the same here<BR>\n" );
document.write( "100a - 10a + 10b - 100b + c - c = 90<BR>\n" );
document.write( "90a - 90b = 90<BR>\n" );
document.write( "divide by 90<BR>\n" );
document.write( "a - b = 1<BR>\n" );
document.write( "b = a - 1; use for substitution<BR>\n" );
document.write( ":<BR>\n" );
document.write( "The difference between the first and third digits is equal to the second digit.<BR>\n" );
document.write( "a - c = b<BR>\n" );
document.write( "Replace replace c with (a-2); replace b with (a-1)<BR>\n" );
document.write( "a - (a-2) = a - 1<BR>\n" );
document.write( "a - a + 2 = a - 1<BR>\n" );
document.write( "2 + 1 = a<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "then using our equations replace a with 3<BR>\n" );
document.write( "c = 3 -2<BR>\n" );
document.write( "c = 1<BR>\n" );
document.write( "and<BR>\n" );
document.write( "b = 3 - 1<BR>\n" );
document.write( "b = 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "321 is the original number<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if that works in the statement,\" If the first and second digits of the original are interchanged the new one is 90 less than the original<BR>\n" );
document.write( "321 - 231 = 90\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );