document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=7795>Question 7795</A>: <I><SPAN STYLE=\"word-break: break-all;\"> When the digits of a two-digit number are reversed, the new number is 9 more than the original number, and the sum of the digits of the original number is 11.  What is the original number?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #4290 by </B><A HREF=/tutors/aboutme.mpl?userid=prince_abubu><B>prince_abubu(198)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=prince_abubu><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=4290\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When we have a two digit number, it can be expressed as 10a + b. Actually, let's take the number 82. That's 80 + 2 which really is 10*8 + 2. The a = 8, and the b = 2.\r<BR>\n" );
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document.write( "So, let's say that we don't know the original 2-digit number. We have to represent that as 10a + b.\r<BR>\n" );
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document.write( "The first thing they say is that when the digits are reversed, the new number is 9 more than the original number. If you reverse the digits of 10a + b, it will be 10b + a. They said that new number is 9 more. This means that the new number is greater, which then means that we must add 9 to the old number so that it will equal the new number. OLD + 9 = NEW. OLD was the 10a + b and NEW was the 10b + a. Let's plug those in: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%2810a+%2B+b%29+%2B+9+=+10b+%2B+a+ ALIGN=MIDDLE  ALT=\"+%2810a+%2B+b%29+%2B+9+=+10b+%2B+a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <----- Relationship between a two digit number and the number that results in reversing the digits.\r<BR>\n" );
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document.write( "They said that the sum of the digits of the original number is 11. So a + b = 11. Let's solve for b: b = 11 - a. Now substitute 11 - a for b in the big equation:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+10a+%2B+%2811+-+a%29+%2B+9+=+10%2811+-+a%29+%2B+a+ ALIGN=MIDDLE  ALT=\"+10a+%2B+%2811+-+a%29+%2B+9+=+10%2811+-+a%29+%2B+a+\"   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=+9a+%2B+20+=+110+-+9a+ ALIGN=MIDDLE  ALT=\"+9a+%2B+20+=+110+-+9a+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- Simplified\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+18a+=+90+ ALIGN=MIDDLE  ALT=\"+18a+=+90+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- added 9a to both sides and subtracted 20 from both sides.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+a+=+5+ ALIGN=MIDDLE  ALT=\"+a+=+5+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---- if a + b = 11, and a = 5, then b must be 6. If a = 5 and b = 6, 10a + b would give you 56, the original number. If you reverse 56, you get 65, which indeed is 9 more than the original number. </SPAN>\n" );
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