document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1164624>Question 1164624</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Raymond is 12 years younger than Susan.  Four years ago, she was 4 times as old as he was.   Find their present ages.  \r<BR>\n" );
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document.write( "I know that right now, Susan is x and Raymond is x-12.  4 years ago, Susan is 4(x-12).  I'm not sure how to set the problem up after this.  Please help.  TY! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #789086 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=789086\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Let me use the work you show to demonstrate what gives beginning algebra students difficulty in setting up problems for solving using algebra.<br><BR>\n" );
document.write( "Here is what you say:<br><BR>\n" );
document.write( "I know that right now, Susan is x and Raymond is x-12.<BR>\n" );
document.write( "4 years ago, Susan is 4(x-12).<BR>\n" );
document.write( "I'm not sure how to set the problem up after this.<br><BR>\n" );
document.write( "In your first line, you use the first sentence of the problem to define expressions for the ages of Raymond and Susan.  Good start.<br><BR>\n" );
document.write( "In the second line, you try to use the statement that 4 years ago she was 4 times as he was then; unfortunately, the equation you write says that her age 4 years ago was 4 times as old as he is NOW.<br><BR>\n" );
document.write( "The step that a lot of beginning students skip is this: the second sentence of the problem talks about their ages 4 years ago -- so you need to find expressions for those.<br><BR>\n" );
document.write( "So, given your definitions of their current ages, you need to note (i.e., write on the paper on which you are working on the problem!) that their ages 4 years ago were x-4 for Susan and (x-12)-4 = x-16 for Raymond.<br><BR>\n" );
document.write( "NOW you have expressions for both their ages 4 years ago; so now you can write the equation that says 4 years ago Susan's age was 4 times Raymond's age:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-4+=+4%28x-16%29 ALIGN=MIDDLE  ALT=\"x-4+=+4%28x-16%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-4+=+4x-64 ALIGN=MIDDLE  ALT=\"x-4+=+4x-64\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60+=+3x ALIGN=MIDDLE  ALT=\"60+=+3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+20 ALIGN=MIDDLE  ALT=\"x+=+20\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: Susan's age is x=20; Raymond's age is x-12 = 8.<br><BR>\n" );
document.write( "CHECK: 4 years ago Susan was 16 and Raymond was 4; 16 is 4 times 4.<br><BR>\n" );
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