document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=158041>Question 158041</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me:\r<BR>\n" );
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document.write( "the sum of the digits of a two-digit number is 12. if the digits are reversed, the new number is 15 more than twice the original number. what is 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 #116451 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=116451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let t=tens digit and u=units digit\r<BR>\n" );
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document.write( "ANY two digit number can be written in the form of: tens_digit*10+units_digit\r<BR>\n" );
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document.write( "Algebraically this looks like: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10t%2Bu ALIGN=MIDDLE  ALT=\"n=10t%2Bu\"   DISABLED_style= \"max-width:90%; height:auto;\" > where \"n\" is any two digit number\r<BR>\n" );
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document.write( "If you reverse the digits of \"n\" you get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=10u%2Bt ALIGN=MIDDLE  ALT=\"m=10u%2Bt\"   DISABLED_style= \"max-width:90%; height:auto;\" > where \"m\" is the reversed number (ie if n=27 then m=72)\r<BR>\n" );
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document.write( "Since the \"sum of the digits of a two-digit number is 12\", this means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Bu=12 ALIGN=MIDDLE  ALT=\"t%2Bu=12\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Also, since the \"new number is 15 more than twice the original number\", this tells us that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10u%2Bt=2%2810t%2Bu%29%2B15 ALIGN=MIDDLE  ALT=\"10u%2Bt=2%2810t%2Bu%29%2B15\"   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=10u%2Bt=20t%2B2u%2B15 ALIGN=MIDDLE  ALT=\"10u%2Bt=20t%2B2u%2B15\"   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=10u%2Bt-20t-2u=15 ALIGN=MIDDLE  ALT=\"10u%2Bt-20t-2u=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20t ALIGN=MIDDLE  ALT=\"20t\"   DISABLED_style= \"max-width:90%; height:auto;\" > from both sides. Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2u ALIGN=MIDDLE  ALT=\"2u\"   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=8u-19t=15 ALIGN=MIDDLE  ALT=\"8u-19t=15\"   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=-19t%2B8u=15 ALIGN=MIDDLE  ALT=\"-19t%2B8u=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rearrange the terms.\r<BR>\n" );
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document.write( "So we have the system:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28t%2Bu=12%2C-19t%2B8u=15%29 ALIGN=MIDDLE  ALT=\"system%28t%2Bu=12%2C-19t%2B8u=15%29\"   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=19%28t%2Bu%29=19%2812%29 ALIGN=MIDDLE  ALT=\"19%28t%2Bu%29=19%2812%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply the both sides of the first equation by 19.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19t%2B19u=228 ALIGN=MIDDLE  ALT=\"19t%2B19u=228\"   DISABLED_style= \"max-width:90%; height:auto;\" > Distribute and multiply.\r<BR>\n" );
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document.write( "So we have the new system of equations:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%2819t%2B19u=228%2C-19t%2B8u=15%29 ALIGN=MIDDLE  ALT=\"system%2819t%2B19u=228%2C-19t%2B8u=15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2819t%2B19u%29%2B%28-19t%2B8u%29=%28228%29%2B%2815%29 ALIGN=MIDDLE  ALT=\"%2819t%2B19u%29%2B%28-19t%2B8u%29=%28228%29%2B%2815%29\"   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=%2819t%2B-19t%29%2B%2819u%2B8u%29=228%2B15 ALIGN=MIDDLE  ALT=\"%2819t%2B-19t%29%2B%2819u%2B8u%29=228%2B15\"   DISABLED_style= \"max-width:90%; height:auto;\" > Group like terms.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0t%2B27u=243 ALIGN=MIDDLE  ALT=\"0t%2B27u=243\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms. Notice how the x terms cancel out.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27u=243 ALIGN=MIDDLE  ALT=\"27u=243\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=%28243%29%2F%2827%29 ALIGN=MIDDLE  ALT=\"u=%28243%29%2F%2827%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=27 ALIGN=MIDDLE  ALT=\"27\"   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=9 ALIGN=MIDDLE  ALT=\"u=9\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "------------------------------------------------------------------\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19t%2B19u=228 ALIGN=MIDDLE  ALT=\"19t%2B19u=228\"   DISABLED_style= \"max-width:90%; height:auto;\" > Now go 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=19t%2B19%289%29=228 ALIGN=MIDDLE  ALT=\"19t%2B19%289%29=228\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=9 ALIGN=MIDDLE  ALT=\"u=9\"   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=19t%2B171=228 ALIGN=MIDDLE  ALT=\"19t%2B171=228\"   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=19t=228-171 ALIGN=MIDDLE  ALT=\"19t=228-171\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=171 ALIGN=MIDDLE  ALT=\"171\"   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=19t=57 ALIGN=MIDDLE  ALT=\"19t=57\"   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=t=%2857%29%2F%2819%29 ALIGN=MIDDLE  ALT=\"t=%2857%29%2F%2819%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=19 ALIGN=MIDDLE  ALT=\"19\"   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=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Reduce.\r<BR>\n" );
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document.write( "So our answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=3 ALIGN=MIDDLE  ALT=\"t=3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=u=9 ALIGN=MIDDLE  ALT=\"u=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "This means that the original number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=10%283%29%2B9=39 ALIGN=MIDDLE  ALT=\"n=10%283%29%2B9=39\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the new number is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m=10%289%29%2B3=93 ALIGN=MIDDLE  ALT=\"m=10%289%29%2B3=93\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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