document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1178360>Question 1178360</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ann, Ben and Cathy have their birthdays today. The sum of their ages is 23. The product of their ages is 113 more than the product of their ages on their birthday last year. What is the sum of the squares of their ages? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #807603 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=807603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x+y+z=23\r<BR>\n" );
document.write( "\n" );
document.write( "xyz=113+(x-1)(y-1)(z-1)\r<BR>\n" );
document.write( "\n" );
document.write( "xyz = 113 +( xy-x-y+1)(z-1)\r<BR>\n" );
document.write( "\n" );
document.write( "xyz= 113+ xyz-xy-xz+x-yz+y+z-1    (xyz) cancels off\r<BR>\n" );
document.write( "\n" );
document.write( "xy+yz+zx =113+22\r<BR>\n" );
document.write( "\n" );
document.write( "xy+yz+zx = 135<BR>\n" );
document.write( "2(xy+yz+zx) =270\r<BR>\n" );
document.write( "\n" );
document.write( "x^2+y^2+z^2=(x+y+z)^2-2(xy+yz+zx)\r<BR>\n" );
document.write( "\n" );
document.write( "= 23^2-270 -259\r<BR>\n" );
document.write( "\n" );
document.write( "the sum of the squares of their ages =259\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );