document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=68859>Question 68859</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The value of a certain 2 digit number is 5 times the sum of its digits. If the digits are reversed,the resulting number 9 more than the original number . Find the original number. T is supposed to represent the tens, and U is supposed to represent the unit. Help. Need to write out this equation and solve it. Spent 3 hours already!! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #49009 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=49009\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The value of a certain 2 digit number is 5 times the sum of its digits. If the digits are reversed,the resulting number 9 more than the original number . Find the original number. T is supposed to represent the tens, and U is supposed to represent the unit.<BR>\n" );
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document.write( "Value = 10T+U   (Just like 32 = 10(3)+2)<BR>\n" );
document.write( "5 times sum of its digits = 5(T+U)<BR>\n" );
document.write( "If digits are reversed Value = 10U+T<BR>\n" );
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document.write( "EQUATIONS:<BR>\n" );
document.write( "1st: 10T+U=5(T+U)<BR>\n" );
document.write( "2nd: 10U+T = 10T+U+9<BR>\n" );
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document.write( "Rewrite the equations:<BR>\n" );
document.write( "1st becomes: 5T-4U=0<BR>\n" );
document.write( "2nd becomes: 9T-9U+9=0<BR>\n" );
document.write( "2nd again: T-U=-1<BR>\n" );
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document.write( "Rewriting the two equations:<BR>\n" );
document.write( "1st: 5T-4U=0<BR>\n" );
document.write( "2nd:T-U=-1<BR>\n" );
document.write( "Solve 2nd for T to get:<BR>\n" );
document.write( "3rd: T=U-1<BR>\n" );
document.write( "Substitute into 1st to get:<BR>\n" );
document.write( "5(U-1)-4U=0<BR>\n" );
document.write( "U=1<BR>\n" );
document.write( "Substitute that into 3rd to get:<BR>\n" );
document.write( "T=1-1=0<BR>\n" );
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document.write( "The two digit number is 01<BR>\n" );
document.write( "When you reverse it you get 10 which is 9 more than the original.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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