document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=92711>Question 92711</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A 2 digit numberis 6 less than 4 times the sum of its digits. If digits are interchange, the new number is 5 less than 8 times the sum of its digits. What's 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 #67486 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=67486\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A 2 digit numberis 6 less than 4 times the sum of its digits. If digits are interchange, the new number is 5 less than 8 times the sum of its digits. What's the original number?<BR>\n" );
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document.write( "Comment: Any two digit number can be written as 10t+u where t is the ten's <BR>\n" );
document.write( "digit and u is the unit's digit.<BR>\n" );
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document.write( "EQUATIONS:<BR>\n" );
document.write( "10t+u+6 = 4(t+u)<BR>\n" );
document.write( "10u+t+5 = 8(t+u)<BR>\n" );
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document.write( "Simplify each equation to get:<BR>\n" );
document.write( "6t-3u=-6<BR>\n" );
document.write( "7t-2u= 5<BR>\n" );
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document.write( "Multiply thru the 1st by 2; Multiply thru the 2nd by 3<BR>\n" );
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document.write( "12t-6u = -12<BR>\n" );
document.write( "21t-6u = 15<BR>\n" );
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document.write( "Subtract the 1st from the 2nd to get:<BR>\n" );
document.write( "9t = 27<BR>\n" );
document.write( "t = 3<BR>\n" );
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document.write( "Substitute into 6t-3u=-6 to solve for u:<BR>\n" );
document.write( "18 - 3u = -6<BR>\n" );
document.write( "3u = 24<BR>\n" );
document.write( "u = 8<BR>\n" );
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document.write( "the original number is 38<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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