document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=946177>Question 946177</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A two digit number is 54 more than the number formed by interchanging the digits the difference between the product and the sum of the digits is 15. Find 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 #577334 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=577334\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> let a = the 10's digit<BR>\n" );
document.write( "let b = the units<BR>\n" );
document.write( "then<BR>\n" );
document.write( "10a + b = the number<BR>\n" );
document.write( "and<BR>\n" );
document.write( "10b + a = the number with digits reversed<BR>\n" );
document.write( ":<BR>\n" );
document.write( "A two digit number is 54 more than the number formed by interchanging the digits<BR>\n" );
document.write( "10a + b = 10b + a + 54<BR>\n" );
document.write( "10a - a = 10b - b + 54<BR>\n" );
document.write( "9a = 9b + 54<BR>\n" );
document.write( "simplify, divide by 9<BR>\n" );
document.write( "a = b + 6<BR>\n" );
document.write( ":<BR>\n" );
document.write( " the difference between the product and the sum of the digits is 15.<BR>\n" );
document.write( "ab - (a+b) = 15<BR>\n" );
document.write( "replace a with (b+6)<BR>\n" );
document.write( "b(b+6) - ((b+6)+b) = 15<BR>\n" );
document.write( "b^2 + 6b - (2b + 6) = 15<BR>\n" );
document.write( "combine like terms<BR>\n" );
document.write( "b^2 + 6b - 2b - 6 - 15 = 0<BR>\n" );
document.write( "b^2 + 4b - 21 = 0<BR>\n" );
document.write( "Factors to<BR>\n" );
document.write( "(b + 7)(b - 3) = 0<BR>\n" );
document.write( "The positive solution is what we want here<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "Find a<BR>\n" );
document.write( "a = 3 + 6<BR>\n" );
document.write( "a = 9<BR>\n" );
document.write( ":<BR>\n" );
document.write( "93 is the number.<BR>\n" );
document.write( ":<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Check this in the statement:<BR>\n" );
document.write( "\"A two digit number is 54 more than the number formed by interchanging the digits \"<BR>\n" );
document.write( "93 = 39 + 54<BR>\n" );
document.write( ":<BR>\n" );
document.write( "You can check it in the other statement<BR>\n" );
document.write( "\" the difference between the product and the sum of the digits is 15.  </SPAN>\n" );
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