document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=772235>Question 772235</A>: <I><SPAN STYLE=\"word-break: break-all;\"> the square of my youngest child's age is 9 more then the product of 17 and the age of my oldest child. my oldest child is 3 years older than my youngest child. How old are my children?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #470793 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=470793\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" >= age of youngest child<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y ALIGN=MIDDLE  ALT=\"y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= age of oldest child<BR>\n" );
document.write( "So<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the square of the youngest child's age<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17y ALIGN=MIDDLE  ALT=\"17y\"   DISABLED_style= \"max-width:90%; height:auto;\" >= the product of 17 and the age of the oldest child<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=17y%2B9 ALIGN=MIDDLE  ALT=\"17y%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 9 more then the product of 17 and the age of the oldest child<BR>\n" );
document.write( "\"The square of my youngest child's age is 9 more then the product of 17 and the age of my oldest child\" translates as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=17y%2B9 ALIGN=MIDDLE  ALT=\"x%5E2=17y%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "\"My oldest child is 3 years older than my youngest child\" translates as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B3 ALIGN=MIDDLE  ALT=\"y=x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "We need to solve the system<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28x%5E2=17y%2B9%2Cy=x%2B3%29 ALIGN=MIDDLE  ALT=\"system%28x%5E2=17y%2B9%2Cy=x%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Substituting <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B3 ALIGN=MIDDLE  ALT=\"y=x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" > into the other equation we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=17%28x%2B3%29%2B9 ALIGN=MIDDLE  ALT=\"x%5E2=17%28x%2B3%29%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=17x%2B51%2B9 ALIGN=MIDDLE  ALT=\"x%5E2=17x%2B51%2B9\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2=17x%2B60 ALIGN=MIDDLE  ALT=\"x%5E2=17x%2B60\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-17x-60=0 ALIGN=MIDDLE  ALT=\"x%5E2-17x-60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That quadratic equation can be solved several ways.<BR>\n" );
document.write( "For me, the easiest way is by factoring:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-17x-60=0 ALIGN=MIDDLE  ALT=\"x%5E2-17x-60=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-20%29%28x%2B3%29=0 ALIGN=MIDDLE  ALT=\"%28x-20%29%28x%2B3%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The solutions are:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-20=0 ALIGN=MIDDLE  ALT=\"x-20=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=20%29 ALIGN=MIDDLE  ALT=\"highlight%28x=20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B3=0 ALIGN=MIDDLE  ALT=\"x%2B3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-3 ALIGN=MIDDLE  ALT=\"x=-3\"   DISABLED_style= \"max-width:90%; height:auto;\" >, which does not make sense, because no person can have a negative age.<BR>\n" );
document.write( "From <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=20%29 ALIGN=MIDDLE  ALT=\"highlight%28x=20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%2B3 ALIGN=MIDDLE  ALT=\"y=x%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >), we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=20%2B3 ALIGN=MIDDLE  ALT=\"y=20%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" >--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=23%29 ALIGN=MIDDLE  ALT=\"highlight%28y=23%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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