document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=561655>Question 561655</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the sum of the digits of a 3-digit number is 14. the hundred's digit being four times the unit's digit. if 594 is subtracted from the number, the number will be reversed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #364462 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=364462\">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" );
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document.write( "write an equation for each statement:<BR>\n" );
document.write( ":<BR>\n" );
document.write( "\"the sum of the digits of a 3-digit number is 14.\"<BR>\n" );
document.write( "a + b + c = 14<BR>\n" );
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document.write( "\"the hundred's digit being four times the unit's digit.\"<BR>\n" );
document.write( "a = 4c<BR>\n" );
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document.write( "\" if 594 is subtracted from the number, the number will be reversed.\"<BR>\n" );
document.write( "100a + 10b + c - 594 = 100c + 10b + a<BR>\n" );
document.write( "100a - a + 10b - 10b = 100c - c + 594<BR>\n" );
document.write( "99a = 99c + 594<BR>\n" );
document.write( "simplify, divide by 99<BR>\n" );
document.write( "a = c + 6<BR>\n" );
document.write( "replace a with 4c<BR>\n" );
document.write( "4c = c + 6<BR>\n" );
document.write( "4c - c = 6<BR>\n" );
document.write( "3c = 6<BR>\n" );
document.write( "c = 2 is the units<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a = 4(2)<BR>\n" );
document.write( "a = 8 is the 100's<BR>\n" );
document.write( ":<BR>\n" );
document.write( "then<BR>\n" );
document.write( " b = 14 - 2 - 8 <BR>\n" );
document.write( "b = 4 is 10s<BR>\n" );
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document.write( "842 is the number<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "See if that works in the statement:<BR>\n" );
document.write( "\"if 594 is subtracted from the number, the number will be reversed.\"<BR>\n" );
document.write( "842 - 594 = 248<BR>\n" );
document.write( "248 = 248 </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );