document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=129733>Question 129733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My daughter is having a tough time with this equation.  \r<BR>\n" );
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document.write( "Fifteen years ago, Alberto was twice as old a Rosa. In nine more years, he will be twice as old as she was when he was as old as she is now.  How old is Rosa?\r<BR>\n" );
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document.write( "Any help is appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #94768 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=94768\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> All of these type problems can be solved this way:<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Alberto's age now<BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > = Rosa's age now<BR>\n" );
document.write( "In order to talk about their ages 15 years ago,<BR>\n" );
document.write( "you have to subtract 15 from EACH of their ages<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+-+15+=+2%28r+-+15%29 ALIGN=MIDDLE  ALT=\"a+-+15+=+2%28r+-+15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The next part is very tricky, and I sort of<BR>\n" );
document.write( "take it one or two words at a time<BR>\n" );
document.write( "It's about Alberto in 9 more years. That's<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+9 ALIGN=MIDDLE  ALT=\"a+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "He's going to be twice as old as something, so<BR>\n" );
document.write( "I've got <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+9 ALIGN=MIDDLE  ALT=\"a+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >= 2 x ?<BR>\n" );
document.write( "Now I've got the brain-twister<BR>\n" );
document.write( "\"twice as old as she was when he was as old as she is now.\"<BR>\n" );
document.write( "I can grapple with it better if I put actual numbers on their<BR>\n" );
document.write( "ages, just for now.<BR>\n" );
document.write( "Say he is 10 and she is 6 now<BR>\n" );
document.write( "4 years ago he was 6 like she is now. Call this age <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D ALIGN=MIDDLE  ALT=\"a%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+a+-+%28a-r%29 ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+a+-+%28a-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5B2%5D+=+r ALIGN=MIDDLE  ALT=\"a%5B2%5D+=+r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is her age now, or 6 years old<BR>\n" );
document.write( "This is \"when he was as old as she is now.\"<BR>\n" );
document.write( "Now how old was she?<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+r+-+%28a+-+r%29 ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+r+-+%28a+-+r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D+=+2r+-+a ALIGN=MIDDLE  ALT=\"r%5B2%5D+=+2r+-+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is \"as old as she was\", or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2A6+-+10+=+2 ALIGN=MIDDLE  ALT=\"2%2A6+-+10+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I put it all together<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+9+=+2%282r+-+a%29 ALIGN=MIDDLE  ALT=\"a+%2B+9+=+2%282r+-+a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+9+=+4r+-+2a ALIGN=MIDDLE  ALT=\"a+%2B+9+=+4r+-+2a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(1) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r+-+3a+=+9 ALIGN=MIDDLE  ALT=\"4r+-+3a+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and from above,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+-+15+=+2%28r+-+15%29 ALIGN=MIDDLE  ALT=\"a+-+15+=+2%28r+-+15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+-+15+=+2r+-+30 ALIGN=MIDDLE  ALT=\"a+-+15+=+2r+-+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r+-+a+=+15 ALIGN=MIDDLE  ALT=\"2r+-+a+=+15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "multiply (2) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2 ALIGN=MIDDLE  ALT=\"2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and subtract from (1)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r+-+3a+=+9 ALIGN=MIDDLE  ALT=\"4r+-+3a+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4r+%2B+2a+=+-30 ALIGN=MIDDLE  ALT=\"-4r+%2B+2a+=+-30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-a+=+-21 ALIGN=MIDDLE  ALT=\"-a+=+-21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+=+21 ALIGN=MIDDLE  ALT=\"a+=+21\"   DISABLED_style= \"max-width:90%; height:auto;\" > Alberto's age now<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r+-+3%2A21+=+9 ALIGN=MIDDLE  ALT=\"4r+-+3%2A21+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r+=+63+%2B+9 ALIGN=MIDDLE  ALT=\"4r+=+63+%2B+9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4r+=+72 ALIGN=MIDDLE  ALT=\"4r+=+72\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+18 ALIGN=MIDDLE  ALT=\"r+=+18\"   DISABLED_style= \"max-width:90%; height:auto;\" > Rosa's age now<BR>\n" );
document.write( "check answers<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+-+15+=+2%28r+-+15%29 ALIGN=MIDDLE  ALT=\"a+-+15+=+2%28r+-+15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21+-+15+=+2%2818+-+15%29 ALIGN=MIDDLE  ALT=\"21+-+15+=+2%2818+-+15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+2%2A3 ALIGN=MIDDLE  ALT=\"6+=+2%2A3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6+=+6 ALIGN=MIDDLE  ALT=\"6+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a+%2B+9+=+2%282r+-+a%29 ALIGN=MIDDLE  ALT=\"a+%2B+9+=+2%282r+-+a%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21+%2B+9+=+2%282%2A18+-+21%29 ALIGN=MIDDLE  ALT=\"21+%2B+9+=+2%282%2A18+-+21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+2%2836+-+21%29 ALIGN=MIDDLE  ALT=\"30+=+2%2836+-+21%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+2%2A15 ALIGN=MIDDLE  ALT=\"30+=+2%2A15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=30+=+30 ALIGN=MIDDLE  ALT=\"30+=+30\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "OK<BR>\n" );
document.write( "whew! </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );