document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=711069>Question 711069</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If agnes is three times as old and joseph and their combined ages is 64, how old is agnes </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #437288 by </B><A HREF=/tutors/aboutme.mpl?userid=tutor_paul><B>tutor_paul(519)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=tutor_paul><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=tutor_paul><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=437288\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The key to this problem is translating the words into equations. Let's take it one phrase at a time. \"agnes is three times as old and joseph.\"<BR>\n" );
document.write( "Let A=Agnes' Age<BR>\n" );
document.write( "Let J=Joseph's Age<BR>\n" );
document.write( "You can represent the above words as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=3J ALIGN=MIDDLE  ALT=\"A=3J\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now let's take the second phrase: \"their combined ages is 64.\"<BR>\n" );
document.write( "You can represent these words as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BJ=64 ALIGN=MIDDLE  ALT=\"A%2BJ=64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "----------------<BR>\n" );
document.write( "Now you have 2 equations and 2 unknown variables. Anytime you have as many equations as unknowns, you can solve the problem!<BR>\n" );
document.write( "To do so, Substitute the expression for A in the first equation above into the second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3J%2BJ=64 ALIGN=MIDDLE  ALT=\"3J%2BJ=64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for J:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4J=64 ALIGN=MIDDLE  ALT=\"4J=64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28J=16%29 ALIGN=MIDDLE  ALT=\"highlight%28J=16%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To find A, substitute the value for J into the first equation, and solve for A. I will leave that part to you.<BR>\n" );
document.write( "===================<BR>\n" );
document.write( "Good Luck,<BR>\n" );
document.write( "tutor_paul@yahoo.com<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );