document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=902053>Question 902053</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of the digits of a three digit number is 13. when 11 is subtracted from the sum of the hundreds digit and tens digit, the answer is equal to the units digit. additionally, when the digits are reversed, the new value is 495 less than 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 #547216 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=547216\">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 digit<BR>\n" );
document.write( "let c = the units<BR>\n" );
document.write( "then<BR>\n" );
document.write( "100a + 10b + c = the value of the 3 digit number<BR>\n" );
document.write( ":<BR>\n" );
document.write( "write an equation for each statement<BR>\n" );
document.write( ":<BR>\n" );
document.write( "the sum of the digits of a three digit number is 13.<BR>\n" );
document.write( "a + b + c = 13<BR>\n" );
document.write( ":<BR>\n" );
document.write( "when 11 is subtracted from the sum of the hundreds digit and tens digit, the answer is equal to the units digit.<BR>\n" );
document.write( "(a+b) - 11 = c<BR>\n" );
document.write( "we can rearrange it<BR>\n" );
document.write( "a + b - c = 11<BR>\n" );
document.write( ":<BR>\n" );
document.write( " additionally, when the digits are reversed, the new value is 495 less than the original number.<BR>\n" );
document.write( "100c + 10b + a = 100a + 10b + c - 495<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "100c - c + 10b - 10b + a - 100a = -495<BR>\n" );
document.write( "99c - 99a = -495<BR>\n" );
document.write( "simplify divide by 99<BR>\n" );
document.write( "c - a = -5<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Use elimination with the 1st two equations<BR>\n" );
document.write( "a + b + c = 13<BR>\n" );
document.write( "a + b - c = 11<BR>\n" );
document.write( "---------------Subtraction eliminates a and b, find c<BR>\n" );
document.write( "2c = 1<BR>\n" );
document.write( "c = 1<BR>\n" );
document.write( "replace c with 1 in the last equation<BR>\n" );
document.write( "1 - a = -5<BR>\n" );
document.write( "-a = -5 - 1<BR>\n" );
document.write( "-a = -6<BR>\n" );
document.write( "a = 6<BR>\n" );
document.write( "Find b<BR>\n" );
document.write( "6 + b + 1 = 13<BR>\n" );
document.write( "b = 13 - 7<BR>\n" );
document.write( "b = 6<BR>\n" );
document.write( ":<BR>\n" );
document.write( "661 is the original number<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if the works<BR>\n" );
document.write( "subtract<BR>\n" );
document.write( "661<BR>\n" );
document.write( "166<BR>\n" );
document.write( "----<BR>\n" );
document.write( "495 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );