document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=636706>Question 636706</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a bag containing only blue, red and green marbles, all but 15 are blue, all but<BR>\n" );
document.write( "13 are red and all but 12 are green. How many are red?<BR>\n" );
document.write( "1. 13<BR>\n" );
document.write( "2. 7<BR>\n" );
document.write( "3. 25<BR>\n" );
document.write( "4. 20 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #401189 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=401189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the number of red marbles be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Let the number of green marbles be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g ALIGN=MIDDLE  ALT=\"g\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Let the number of blue marbles be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "All the marbles means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Bb%2Bg ALIGN=MIDDLE  ALT=\"r%2Bb%2Bg\"   DISABLED_style= \"max-width:90%; height:auto;\" > marbles.<BR>\n" );
document.write( "The fact that all but 15 of the marbles are blue means that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Bg=15 ALIGN=MIDDLE  ALT=\"r%2Bg=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > (15 of those marbles are either red or green).<BR>\n" );
document.write( "The fact that all but 13 of the marbles are red means that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=g%2Bb=13 ALIGN=MIDDLE  ALT=\"g%2Bb=13\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The fact that all but 12 of the marbles are green means that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Bb=12 ALIGN=MIDDLE  ALT=\"r%2Bb=12\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We have a system of 3 linear equations with 3 variables:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28r%2Bg=15%2Cg%2Bb=13%2Cr%2Bb=12%29 ALIGN=MIDDLE  ALT=\"system%28r%2Bg=15%2Cg%2Bb=13%2Cr%2Bb=12%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtracting the second equation from the first, we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Bg-%28g%2Bb%29=15-13 ALIGN=MIDDLE  ALT=\"r%2Bg-%28g%2Bb%29=15-13\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Bg-g-b=2 ALIGN=MIDDLE  ALT=\"r%2Bg-g-b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-b=2 ALIGN=MIDDLE  ALT=\"r-b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Adding that to the third equation we get<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Bb%2B%28r-b%29=12%2B2 ALIGN=MIDDLE  ALT=\"r%2Bb%2B%28r-b%29=12%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2Bb%2Br-b=14 ALIGN=MIDDLE  ALT=\"r%2Bb%2Br-b=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r=14 ALIGN=MIDDLE  ALT=\"2r=14\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r%2F2=14%2F2 ALIGN=MIDDLE  ALT=\"2r%2F2=14%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28r=7%29 ALIGN=MIDDLE  ALT=\"highlight%28r=7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );