document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187483>Question 1187483</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If Anne is 4 years older than Marie and the sum of the squares of their ages is 40. what are their individual ages? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818493 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13203)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=818493\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Solving by trial and error is far easier than a formal algebraic solution.  Simply look for a way to break 40 into the sum of two perfect squares.<br><BR>\n" );
document.write( "1+39?  no<BR>\n" );
document.write( "4+36?  YES<br><BR>\n" );
document.write( "The squares of their ages are 4 and 36; their ages are 2 and 6.  6 is 4 more than 2, so that solution works.<br><BR>\n" );
document.write( "But probably a formal algebraic solution was wanted....<br><BR>\n" );
document.write( "Let x = Marie's age<BR>\n" );
document.write( "Then x+4 = Anne's age<br><BR>\n" );
document.write( "The sum of the squares of their ages is 40:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B%28x%2B4%29%5E2=40 ALIGN=MIDDLE  ALT=\"x%5E2%2B%28x%2B4%29%5E2=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2Bx%5E2%2B8x%2B16=40 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%5E2%2B8x%2B16=40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2%2B8x-24=0 ALIGN=MIDDLE  ALT=\"2x%5E2%2B8x-24=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B4x-12=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B4x-12=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B6%29%28x-2%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B6%29%28x-2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-6 ALIGN=MIDDLE  ALT=\"x=-6\"   DISABLED_style= \"max-width:90%; height:auto;\" >  OR  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2 ALIGN=MIDDLE  ALT=\"x=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Obviously the negative solution for Marie's age makes no sense; so x=2.<br><BR>\n" );
document.write( "ANSWERS: Marie's age = x = 2; Anne's age = x+4 = 6<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );