document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172652>Question 172652</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I submitted this question a little earlier.  This is the first time I have ever used this site.  It is great; thank you!  I just read how you like to see work.  Anyway, I did not do that.  So here is the question again:  The sum of the three digits is 12.  The tens digit exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit.  If the digits are reversed, the new number exceeds the original number by 198.  Find the original number.  Here is my work:  H + T + U = 12.  (100u + 10t + h) - (100H + 10T + u) = 198.  The example in the textbook is simple.  This is more complicated.  I've been working at it for some time.  I appreciate you help so much! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127511 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=127511\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> You're on the right track. You have 2 of the three equations needed to solve this problem. Why are 3 equations needed? You have 3 variables, so you need 3 equations. \r<BR>\n" );
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document.write( "Since \"The tens digit exceeds the hundreds digit by the same amount that the units digit exceeds the tens digit\", this means that the third equation is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-h=u-t ALIGN=MIDDLE  ALT=\"t-h=u-t\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t-h=u-t ALIGN=MIDDLE  ALT=\"t-h=u-t\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the third equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=u-t%2Bh ALIGN=MIDDLE  ALT=\"t=u-t%2Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Bt=u%2Bh ALIGN=MIDDLE  ALT=\"t%2Bt=u%2Bh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Bt-u=h ALIGN=MIDDLE  ALT=\"t%2Bt-u=h\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t-u=h ALIGN=MIDDLE  ALT=\"2t-u=h\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2t-u ALIGN=MIDDLE  ALT=\"h=2t-u\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the equation.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+%2B+t+%2B+u+=+12 ALIGN=MIDDLE  ALT=\"h+%2B+t+%2B+u+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move back to the first equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t-u+%2B+t+%2B+u+=+12 ALIGN=MIDDLE  ALT=\"2t-u+%2B+t+%2B+u+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2t-u ALIGN=MIDDLE  ALT=\"h=2t-u\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3t+=+12 ALIGN=MIDDLE  ALT=\"3t+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=%2812%29%2F%283%29 ALIGN=MIDDLE  ALT=\"t=%2812%29%2F%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4 ALIGN=MIDDLE  ALT=\"t=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce. So the tens digit is 4\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2t-u ALIGN=MIDDLE  ALT=\"h=2t-u\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the previously isolated equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=2%284%29-u ALIGN=MIDDLE  ALT=\"h=2%284%29-u\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4 ALIGN=MIDDLE  ALT=\"t=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=8-u ALIGN=MIDDLE  ALT=\"h=8-u\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100u+%2B+10t+%2B+h%29+-+%28100h+%2B+10t+%2B+u%29+=+198 ALIGN=MIDDLE  ALT=\"%28100u+%2B+10t+%2B+h%29+-+%28100h+%2B+10t+%2B+u%29+=+198\"   DISABLED_style= \"max-width:90%; height:auto;\" > Move onto the second equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100u+%2B+10%284%29+%2B+8-u%29+-+%28100%288-u%29+%2B+10%284%29+%2B+u%29+=+198 ALIGN=MIDDLE  ALT=\"%28100u+%2B+10%284%29+%2B+8-u%29+-+%28100%288-u%29+%2B+10%284%29+%2B+u%29+=+198\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=8-u ALIGN=MIDDLE  ALT=\"h=8-u\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4 ALIGN=MIDDLE  ALT=\"t=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28100u+%2B+40+%2B+8-u%29+-+%28100%288-u%29+%2B+40+%2B+u%29+=+198 ALIGN=MIDDLE  ALT=\"%28100u+%2B+40+%2B+8-u%29+-+%28100%288-u%29+%2B+40+%2B+u%29+=+198\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100u+%2B+40+%2B+8-u+-+100%288-u%29+-+40+-+u+=+198 ALIGN=MIDDLE  ALT=\"100u+%2B+40+%2B+8-u+-+100%288-u%29+-+40+-+u+=+198\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute the negative.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100u+%2B+40+%2B+8-u+-+800%2B100u+-+40+-+u+=+198 ALIGN=MIDDLE  ALT=\"100u+%2B+40+%2B+8-u+-+800%2B100u+-+40+-+u+=+198\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=198u-792=198 ALIGN=MIDDLE  ALT=\"198u-792=198\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the left side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=198u=198%2B792 ALIGN=MIDDLE  ALT=\"198u=198%2B792\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=792 ALIGN=MIDDLE  ALT=\"792\"   DISABLED_style= \"max-width:90%; height:auto;\" > to both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=198u=990 ALIGN=MIDDLE  ALT=\"198u=990\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms on the right side.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=%28990%29%2F%28198%29 ALIGN=MIDDLE  ALT=\"u=%28990%29%2F%28198%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=198 ALIGN=MIDDLE  ALT=\"198\"   DISABLED_style= \"max-width:90%; height:auto;\" > to isolate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u ALIGN=MIDDLE  ALT=\"u\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=5 ALIGN=MIDDLE  ALT=\"u=5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce. So the units (or ones) digit is 5\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=8-u ALIGN=MIDDLE  ALT=\"h=8-u\"   DISABLED_style= \"max-width:90%; height:auto;\" > Go back to the isolated equation\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=8-5 ALIGN=MIDDLE  ALT=\"h=8-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=5 ALIGN=MIDDLE  ALT=\"u=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract. So the hundreds digit is 3\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "So the digits are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=3 ALIGN=MIDDLE  ALT=\"h=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=4 ALIGN=MIDDLE  ALT=\"t=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=5 ALIGN=MIDDLE  ALT=\"u=5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "This means that the original number is 345\r<BR>\n" );
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document.write( "Note: I appreciate you showing your work. </SPAN>\n" );
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