document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=551297>Question 551297</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The value of certain two digit number is four less than six times the sum of it's digits. If the digits of the number are reversed, the resulting number is nine less than the original number. Find the number. Please help me!!!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #359604 by </B><A HREF=/tutors/aboutme.mpl?userid=TutorDelphia><B>TutorDelphia(193)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=TutorDelphia><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=TutorDelphia><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=359604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To figure this out logically, for the number to be 9 less when the digits are reversed, they have to be within 1 of each other: for example 23 is 9 less than 32.<BR>\n" );
document.write( "Than we can check 98, 87 ...21, 10 to see which works.\r<BR>\n" );
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document.write( "Algebraically: \r<BR>\n" );
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document.write( "Let's say our two digit number is called XY<BR>\n" );
document.write( "And this is not the answer, but if x is 3 and y is 4 the value of xy is 3*10+4 which is 34. So always multiply the digit in the tens place by 10 to find its value.\r<BR>\n" );
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document.write( "So with that in mind: The value of certain two digit number is four less than six times the sum of it's digits could be expressed as:  <BR>\n" );
document.write( "X*10+y=6*(x+y)-4<BR>\n" );
document.write( "Distribute<BR>\n" );
document.write( "10x+y=6x+6y-4<BR>\n" );
document.write( "subtract 6x-6y from both sides<BR>\n" );
document.write( "4x-5y=-4\r<BR>\n" );
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document.write( "We also know if you reverse the digits the resulting number is nine less. Again, multiply the digit in the tens place by 10<BR>\n" );
document.write( "X*10+y-9=y*10+x<BR>\n" );
document.write( "9x-9y=9\r<BR>\n" );
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document.write( "So now we have the two equations:<BR>\n" );
document.write( "4x-5y=-4<BR>\n" );
document.write( "9x-9y=9<BR>\n" );
document.write( "So we have to multiply the first by 9 and the second by -4<BR>\n" );
document.write( "36x-45y=-36<BR>\n" );
document.write( "-36x+36y=-36<BR>\n" );
document.write( "-9y=-72<BR>\n" );
document.write( "y=8\r<BR>\n" );
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document.write( "Sub in 8 for y<BR>\n" );
document.write( "9*x-9*8=9<BR>\n" );
document.write( "9x-72=9<BR>\n" );
document.write( "9x=81<BR>\n" );
document.write( "x=9<BR>\n" );
document.write( "Try it out<BR>\n" );
document.write( "98 is  4 less than 6 times 15 (102-4=98)<BR>\n" );
document.write( "And 89 is 9 less than 98\r<BR>\n" );
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