document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=148904>Question 148904</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a two digit number is 5 times the sum of its digit.  when 9 is added to the number the result is the original number with its reversed.  find 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 #109221 by </B><A HREF=/tutors/aboutme.mpl?userid=oscargut><B>oscargut(2103)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oscargut><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=oscargut><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109221\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let a and b the digits we can write the number as \"ab\" but the number is 10*a+b<BR>\n" );
document.write( "(for example if a=3 and b=2 the number would be 32 and 32 =10*3+2)\r<BR>\n" );
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document.write( "a two digit number is 5 times the sum of its digit then 10*a+b=5(a+b)<BR>\n" );
document.write( "when 9 is added to the number the result is the original number with its reversed 10*a+b+9=10*b+a\r<BR>\n" );
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document.write( "then we have the following equations:\r<BR>\n" );
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document.write( "10*a+b=5(a+b)<BR>\n" );
document.write( "10*a+b+9=10*b+a\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "10a+b=5a+5b<BR>\n" );
document.write( "10a+b+9=10b+a\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "5a-4b=0<BR>\n" );
document.write( "9a-9b=-9\r<BR>\n" );
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document.write( "then\r<BR>\n" );
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document.write( "5a-4b=0<BR>\n" );
document.write( "a-b=-1\r<BR>\n" );
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document.write( "then using 2nd eq a=b-1\r<BR>\n" );
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document.write( "using 1st eq 5(b-1)-4b=0\r<BR>\n" );
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document.write( "then 5b-5-4b=0<BR>\n" );
document.write( "then b=5 and a=5-1=4\r<BR>\n" );
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document.write( "so the original number is 45\r<BR>\n" );
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document.write( " </SPAN>\n" );
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