document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=690416>Question 690416</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A three-digit number is 198 less than the number when its digits are reversed. twice the sum of the digits is 5 more than 7 times the tens digit. the tens digit is 5 less than twice the hundreds 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 #426433 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=426433\">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 number<BR>\n" );
document.write( "and<BR>\n" );
document.write( "100c+10b+a = the number reversed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"A three-digit number is 198 less than the number when its digits are reversed.\"<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( "a = c - 2<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"twice the sum of the digits is 5 more than 7 times the tens digit.\"<BR>\n" );
document.write( "2(a+b+c) = 7b + 5<BR>\n" );
document.write( "2a + 2b + 2c = 7b + 5<BR>\n" );
document.write( "2a + 2b - 7b + 2c = 5<BR>\n" );
document.write( "2a - 5b + 2c = 5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\" the tens digit is 5 less than twice the hundreds digit.\"<BR>\n" );
document.write( "b = 2a - 5<BR>\n" );
document.write( "replace a with (c-2)<BR>\n" );
document.write( "b = 2(c-2) - 5<BR>\n" );
document.write( "b = 2c - 4 - 5<BR>\n" );
document.write( "b = 2c - 9<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Back to the 2nd statement equation<BR>\n" );
document.write( "2a - 5b + 2c = 5<BR>\n" );
document.write( "replace a with c-2 and replace b with 2c-9<BR>\n" );
document.write( "2(c-2) - 5(2c-9) + 2c = 5<BR>\n" );
document.write( "2c - 4 - 10c + 45 + 2c = 5<BR>\n" );
document.write( "2c - 10c + 2c + 41 = 5<BR>\n" );
document.write( "-6c = 5 - 41<BR>\n" );
document.write( "-6c = -36<BR>\n" );
document.write( "c = 6<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = 6 - 2<BR>\n" );
document.write( "a = 4<BR>\n" );
document.write( "and<BR>\n" );
document.write( "b = 2(6) - 9<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( ":<BR>\n" );
document.write( "436 is the original number<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if that checks out; subtract from the reversed number.<BR>\n" );
document.write( "634<BR>\n" );
document.write( "436<BR>\n" );
document.write( "----Subtract<BR>\n" );
document.write( "198\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );