document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=516819>Question 516819</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Solve-A 2-digit no. Is such that the product of its digits is 18.When 63 is subtracted from the no. the digits interchange their position.Find the nos. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #344514 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=344514\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With digit problems you have to look at a number in terms of the place values of its digits. Consider the number 'xy' which does NOT mean x*y, but rather x being next to y.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The value of 'xy' is 10x + y.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x*y = 18<BR>\n" );
document.write( "so<BR>\n" );
document.write( "x = 18/y<BR>\n" );
document.write( ".<BR>\n" );
document.write( "10x + y -63 = 10y + x<BR>\n" );
document.write( ".<BR>\n" );
document.write( "subsitute<BR>\n" );
document.write( ".<BR>\n" );
document.write( "10*18/y +y -63 = 10y +18/y<BR>\n" );
document.write( ".<BR>\n" );
document.write( "180/y + y -63 = 10y + 18/y<BR>\n" );
document.write( ".<BR>\n" );
document.write( "multiply through by y to eliminate the fractions<BR>\n" );
document.write( ".<BR>\n" );
document.write( "180 + y^2 -63y = 10y^2 + 18<BR>\n" );
document.write( ".<BR>\n" );
document.write( "collect terms<BR>\n" );
document.write( ".<BR>\n" );
document.write( "10y^ + 18 = y^2 -63y + 180<BR>\n" );
document.write( "9y^2 +63y -162 = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "divide by 9<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y^2 +7y - 18 = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "factor<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(y+9)(y-2) = 0<BR>\n" );
document.write( ".<BR>\n" );
document.write( "y = -9 or 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Substitute 2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "x*2 = 18<BR>\n" );
document.write( "x = 9<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The original number appears to be:  92.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "The product of 9*2 = 18, which is how the solution was found.<BR>\n" );
document.write( "To check these values, you have to use the other equation.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "92 - 63 = 29<BR>\n" );
document.write( "Yep. The digits are interchanged.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Answer:  The original number is 92. The other number is 29.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Done.<BR>\n" );
document.write( ".<BR>\n" );
document.write( "But what about the y=-9?<BR>\n" );
document.write( "Well, it is not a single digit.<BR>\n" );
document.write( "x*-9 = 18<BR>\n" );
document.write( "x = -2<BR>\n" );
document.write( ".<BR>\n" );
document.write( "-29 -63 = -92<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So in a sense it works, but we would need a means to show a negative number with a different symbol that takes only one space for this solution to make common sense.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );