document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=33419>Question 33419</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0072934824/algebrahomeworkh>algebra for college students</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> This word problem is stumping me. I can't figure out how to write the equations needed for it. please help.\r<BR>\n" );
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document.write( "The sum of the digits of a three-digit number is 11. If the digits are reversed, the new number is 46 more than 5 times the old number. If the hundreds digit plus twice the tens digit is equal to the units digit, then what is the number? \r<BR>\n" );
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document.write( "I have come up with x+y+z = 11 <BR>\n" );
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document.write( "I'm lost on the second equation. \r<BR>\n" );
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document.write( "and i'm pretty sure the third equation is <BR>\n" );
document.write( "x+2y = z \r<BR>\n" );
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document.write( "I hope I'm at least close. I would appreciate any help.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #19766 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=19766\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the number be xyz. We are told that x+y+z=11\r<BR>\n" );
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document.write( "original number is xyz<BR>\n" );
document.write( "--> xyz really means 100x+10y+z\r<BR>\n" );
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document.write( "Reversing gives zyx<BR>\n" );
document.write( "--> zyx really means 100z+10y+x\r<BR>\n" );
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document.write( "zyx is 46 more than 5 times the old number:\r<BR>\n" );
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document.write( "So, (100z+10y+x) = 5(100x+10y+z) + 46<BR>\n" );
document.write( "--> 100z+10y+x = 500x+50y+5z + 46<BR>\n" );
document.write( "--> 95z-40y-499x = 46\r<BR>\n" );
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document.write( "Also, hundreds digit (x) + twice tens (y) equals units (z)<BR>\n" );
document.write( "--> x + 2y = z\r<BR>\n" );
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document.write( "So, we have 3 unknowns, xy and z and we have 3 equations relating them:\r<BR>\n" );
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document.write( "x+y+z=11<BR>\n" );
document.write( "95z-40y-499x = 46<BR>\n" );
document.write( "x+2y=z\r<BR>\n" );
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document.write( "You try to solve these 3 :-)<BR>\n" );
document.write( "answer is 137 for the number.\r<BR>\n" );
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document.write( "jon.<BR>\n" );
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