document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187418>Question 1187418</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Four times Polly’s present age is 4 more than eight times Olive’s age 2 years ago. Three times Olive’s age is 3 more than twice what Polly’s age was 4 years ago. Find their present ages. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818422 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=818422\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "Define some variables...<br><BR>\n" );
document.write( "Let x = Olive's current age<BR>\n" );
document.write( "Let y = Polly's current age<br><BR>\n" );
document.write( "... and translate each given piece of information directly into an algebraic equation.<br><BR>\n" );
document.write( "Four times Polly’s present age is 4 more than eight times Olive’s age 2 years ago.<br><BR>\n" );
document.write( "Polly's present age is y; Olive's age 2 years ago was x-2:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=8%28x-2%29%2B4 ALIGN=MIDDLE  ALT=\"4y=8%28x-2%29%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=8x-16%2B4 ALIGN=MIDDLE  ALT=\"4y=8x-16%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4y=8x-12 ALIGN=MIDDLE  ALT=\"4y=8x-12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=2x-3 ALIGN=MIDDLE  ALT=\"y=2x-3\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<br><BR>\n" );
document.write( "Three times Olive’s age is 3 more than twice what Polly’s age was 4 years ago.<br><BR>\n" );
document.write( "Olive's age now is x; Polly's age 4 years ago was y-4:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=2%28y-4%29%2B3 ALIGN=MIDDLE  ALT=\"3x=2%28y-4%29%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=2y-8%2B3 ALIGN=MIDDLE  ALT=\"3x=2y-8%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x=2y-5 ALIGN=MIDDLE  ALT=\"3x=2y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > [2]<br><BR>\n" );
document.write( "With the two equations [1] and [2] in those forms, a solution using substitution seems the way to go.  Substitute [1] in [2]:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x+=+2%282x-3%29-5 ALIGN=MIDDLE  ALT=\"3x+=+2%282x-3%29-5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "I'll let you finish.  Solve that equation for x, then substitute the value of x in [1] to find y.<br><BR>\n" );
document.write( " </SPAN>\n" );
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