document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1111032>Question 1111032</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Malcolm’s mother is 27 years older than he is and their ages are both two-digit numbers. If Malcolm swaps the digits in his age, he gets his mother’s age.<BR>\n" );
document.write( "a How old is Malcolm if the sum of the digits in his age is 5?<BR>\n" );
document.write( "b What is the relationship between the digits in Malcolm’s age if the sum of the digits is<BR>\n" );
document.write( "unknown.<BR>\n" );
document.write( "c If the sum of the digits in Malcolm’s two-digit age is unknown, how many possible ages<BR>\n" );
document.write( "could he be? What are these ages?<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #726036 by </B><A HREF=/tutors/aboutme.mpl?userid=mananth><B>mananth(16946)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=mananth><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=mananth><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=726036\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Malcolm’s mother is 27 years older than he is and their ages are both two-digit numbers. If Malcolm swaps the digits in his age, he gets his mother’s age.<BR>\n" );
document.write( "a How old is Malcolm if the sum of the digits in his age is 5?<BR>\n" );
document.write( "b What is the relationship between the digits in Malcolm’s age if the sum of the digits is<BR>\n" );
document.write( "unknown.<BR>\n" );
document.write( "c If the sum of the digits in Malcolm’s two-digit age is unknown, how many possible ages<BR>\n" );
document.write( "could he be? What are these ages?\r<BR>\n" );
document.write( "\n" );
document.write( "let  Malcolm's age be 10x+y<BR>\n" );
document.write( "mothers age is 10x+y+27\r<BR>\n" );
document.write( "\n" );
document.write( "equation after swapping the digits<BR>\n" );
document.write( "10y+x = 10x+y+27<BR>\n" );
document.write( "9y-9x=27<BR>\n" );
document.write( "y-x=3<BR>\n" );
document.write( "x+y=5\r<BR>\n" );
document.write( "\n" );
document.write( "add the equations<BR>\n" );
document.write( "2y=8<BR>\n" );
document.write( "y=4<BR>\n" );
document.write( "therefore x= 1\r<BR>\n" );
document.write( "\n" );
document.write( "Malcom's age = 10x +y = 14<BR>\n" );
document.write( "mother's age = 14+27 = 41<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );