document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183180>Question 1183180</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Aaron is 16 years younger than Angela. 8 years ago, Angela's age was 2 times Aaron's age. How old is Aaron now? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #813367 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</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=813367\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "First, informally....<br><BR>\n" );
document.write( "If Angela is 16 years older than Aaron, then she was twice as old as him when their ages were 32 and 16.<BR>\n" );
document.write( "Since that was 8 years ago, their ages now are 40 and 24.<br><BR>\n" );
document.write( "ANSWER: 24<br><BR>\n" );
document.write( "For one way to set up and solve the problem using formal algebra....<br><BR>\n" );
document.write( "let x = Aaron's age now<BR>\n" );
document.write( "then x+16 = Angela's age now<br><BR>\n" );
document.write( "x-8 = Aaron's age 8 years ago<BR>\n" );
document.write( "(x+16)-8 = x+8 = Angela's age 8 years ago<br><BR>\n" );
document.write( "8 years ago, Angela's age was twice Aaron's age:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B8=2%28x-8%29 ALIGN=MIDDLE  ALT=\"x%2B8=2%28x-8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B8=2x-16 ALIGN=MIDDLE  ALT=\"x%2B8=2x-16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=24 ALIGN=MIDDLE  ALT=\"x=24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: Aaron's age now is x=24<br><BR>\n" );
document.write( "Here is another formal algebraic solution that is like the informal solution above.<br><BR>\n" );
document.write( "Let x = Aaron's age 8 years ago<BR>\n" );
document.write( "Then 2x = Angela's age 8 years ago<br><BR>\n" );
document.write( "The difference in their ages is 16 years:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x-x=16 ALIGN=MIDDLE  ALT=\"2x-x=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=16 ALIGN=MIDDLE  ALT=\"x=16\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Aaron's age 8 years ago was x=16<BR>\n" );
document.write( "Aaron's age now is 16+8=24<br><BR>\n" );
document.write( "Of the two algebraic solutions above, I personally prefer the latter, because the actual algebra is simpler.<br><BR>\n" );
document.write( "Look at both formal solutions, and at any others you might get in responses from other tutors, and find what \"works\" best for you.<br><BR>\n" );
document.write( " </SPAN>\n" );
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