document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=127362>Question 127362</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Frida is five years older than Fredelyn. In three years the product of her age and Fredelyn's age five years ago will be 9o years. zFind 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 #93316 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93316\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Frida's current age is x and Fredelyn's current age is y.\r<BR>\n" );
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document.write( "The first thing we know is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y%2B5 ALIGN=MIDDLE  ALT=\"x=y%2B5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Three years from now Frida will be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3 ALIGN=MIDDLE  ALT=\"x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and five years ago, Fredelyn was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y-5 ALIGN=MIDDLE  ALT=\"y-5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and we know that the product of these two values is 90, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B3%29%28y-5%29=90 ALIGN=MIDDLE  ALT=\"%28x%2B3%29%28y-5%29=90\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Substitute the expression for x in terms of y from the first equation into the second equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28y%2B5%29%2B3%29%28y-5%29=90 ALIGN=MIDDLE  ALT=\"%28%28y%2B5%29%2B3%29%28y-5%29=90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Simplify, expand, and put into standard form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y%2B8%29%28y-5%29=90 ALIGN=MIDDLE  ALT=\"%28y%2B8%29%28y-5%29=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B3y-40=90 ALIGN=MIDDLE  ALT=\"y%5E2%2B3y-40=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y%5E2%2B3y-130=0 ALIGN=MIDDLE  ALT=\"y%5E2%2B3y-130=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-130=%28-10%29%2813%29 ALIGN=MIDDLE  ALT=\"-130=%28-10%29%2813%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=-10%2B13 ALIGN=MIDDLE  ALT=\"3=-10%2B13\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28y-10%29%28y%2B13%29=0 ALIGN=MIDDLE  ALT=\"%28y-10%29%28y%2B13%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >, hence Fredelyn is either 10 or -13 years old.  Since a negative number for the age of a person is absurd, exclude this root.  Fredelyn is therefore 10 years old.\r<BR>\n" );
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document.write( "From equation 1:  Frida is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2B5=15 ALIGN=MIDDLE  ALT=\"10%2B5=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > years old.\r<BR>\n" );
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document.write( "Check:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2815%2B3%29%2810-5%29=18%2A5=90 ALIGN=MIDDLE  ALT=\"%2815%2B3%29%2810-5%29=18%2A5=90\"   DISABLED_style= \"max-width:90%; height:auto;\" > answer checks. </SPAN>\n" );
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