document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=226573>Question 226573</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if a certain two digit number is divided by the sum of its digits, the quotient is 3. if the digits are reversed, the new number is 9 less then three times the original number. find the original number.\r<BR>\n" );
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document.write( "I think i have one of the equations: I used Z as my new number and X as the original number. Z=3X-9<BR>\n" );
document.write( "could you help me solve this using a set of system of equations?\r<BR>\n" );
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document.write( "Thank you. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #168686 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=168686\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let x = original number and y = reversed number\r<BR>\n" );
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document.write( "Any two digit number is of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10t%2Bu ALIGN=MIDDLE  ALT=\"x=10t%2Bu\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Ex: 21=10*2+1 (think of t is the tens digit and u as the units/ones digit)\r<BR>\n" );
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document.write( "So <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10t%2Bu ALIGN=MIDDLE  ALT=\"x=10t%2Bu\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10u%2Bt ALIGN=MIDDLE  ALT=\"y=10u%2Bt\"   DISABLED_style= \"max-width:90%; height:auto;\" > (just swap t and u)\r<BR>\n" );
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document.write( "The statement \"if a certain two digit number is divided by the sum of its digits, the quotient is 3\" translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2F%28t%2Bu%29=3 ALIGN=MIDDLE  ALT=\"x%2F%28t%2Bu%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > (because t+u is the sum of the digits). Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10t%2Bu ALIGN=MIDDLE  ALT=\"x=10t%2Bu\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810t%2Bu%29%2F%28t%2Bu%29=3 ALIGN=MIDDLE  ALT=\"%2810t%2Bu%29%2F%28t%2Bu%29=3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So this is our first equation.\r<BR>\n" );
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document.write( "\"if the digits are reversed, the new number is 9 less then three times the original number\" translates to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x-9 ALIGN=MIDDLE  ALT=\"y=3x-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=10t%2Bu ALIGN=MIDDLE  ALT=\"x=10t%2Bu\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=10u%2Bt ALIGN=MIDDLE  ALT=\"y=10u%2Bt\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10u%2Bt=3%2810t%2Bu%29-9 ALIGN=MIDDLE  ALT=\"10u%2Bt=3%2810t%2Bu%29-9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This is the second equation.\r<BR>\n" );
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document.write( "So you now have the system <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28%2810t%2Bu%29%2F%28t%2Bu%29=3%2C10u%2Bt=3%2810t%2Bu%29-9%29 ALIGN=MIDDLE  ALT=\"system%28%2810t%2Bu%29%2F%28t%2Bu%29=3%2C10u%2Bt=3%2810t%2Bu%29-9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Because you have two equations with two unknowns, you can find the unique solution which means you can find t and u. I'll let you do that. Let me know if you still need help. </SPAN>\n" );
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