document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1124174>Question 1124174</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the first and third digits of a three-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 between 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 #740590 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=740590\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let the 3 digit number = 100a + 10b + c<BR>\n" );
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document.write( "If the first and third digits of a three-digit number are interchanged, the difference between the original number and the new one is 198.<BR>\n" );
document.write( "(100a+10b+c) - (100c+b+a) = 198<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" );
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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( "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( ":<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" );
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document.write( "Find the original number.<BR>\n" );
document.write( "looking at the 1st and 3rd simplified equations we can see that b=2<BR>\n" );
document.write( "Find a<BR>\n" );
document.write( "a - 2 = 1<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "and<BR>\n" );
document.write( "3 - c = 2<BR>\n" );
document.write( "c = 1<BR>\n" );
document.write( "the original number: 321<BR>\n" );
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