document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=147405>Question 147405</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A two digit counting number has a value of 8 times the sum of its digits. If 6 times the units digit is 5 more than the tens digits, what is the number? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #107793 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><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=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=107793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A two digit counting number has a value of 8 times the sum of its digits. If 6 times the units digit is 5 more than the tens digits, what is the number?<BR>\n" );
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document.write( "Let x = \"units\" digit<BR>\n" );
document.write( "and y = \"tens\" digit<BR>\n" );
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document.write( "Since we have two unknowns, we'll need two equations.<BR>\n" );
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document.write( "From:<BR>\n" );
document.write( "\"A two digit counting number has a value of 8 times the sum of its digits.\"<BR>\n" );
document.write( "we get equation 1:<BR>\n" );
document.write( "10y + x = 8(x+y)<BR>\n" );
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document.write( "From:<BR>\n" );
document.write( "\"6 times the units digit is 5 more than the tens digits\"<BR>\n" );
document.write( "we get equation 2:<BR>\n" );
document.write( "6x - 5 = y<BR>\n" );
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document.write( "From equation 2, we see that y is equal to (6x+5) -- substitute this into equation 1 and solve for x:<BR>\n" );
document.write( "10y + x = 8(x+y)<BR>\n" );
document.write( "10(6x-5) + x = 8(x+(6x-5))<BR>\n" );
document.write( "(60x-50) + x = 8(7x-5)<BR>\n" );
document.write( "61x-50 = 56x-40<BR>\n" );
document.write( "5x = 10<BR>\n" );
document.write( "x = 2<BR>\n" );
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document.write( "To find y, substitute the above into equation 2:<BR>\n" );
document.write( "6x - 5 = y<BR>\n" );
document.write( "6(2) - 5 = y<BR>\n" );
document.write( "12 - 5 = y<BR>\n" );
document.write( "7 = y<BR>\n" );
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document.write( "Your 2 digit number is: 72\r<BR>\n" );
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document.write( "  </SPAN>\n" );
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