document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=846445>Question 846445</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Three boys are talking about how many sweets they each have.\r<BR>\n" );
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document.write( "A: B has the most!<BR>\n" );
document.write( "B: If C gave me one sweet, I'd have twice as many as A does.<BR>\n" );
document.write( "C: It'd be better if B gave me two sweets. Then we'd all have the same amount!\r<BR>\n" );
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document.write( "How many sweets are there in total?\r<BR>\n" );
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document.write( "I know the answer but the algebra is giving me trouble. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #509725 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5347)</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=509725\">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=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of sweets A has.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B ALIGN=MIDDLE  ALT=\"B\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of sweets B has.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C ALIGN=MIDDLE  ALT=\"C\"   DISABLED_style= \"max-width:90%; height:auto;\" >= number of sweets C has.<BR>\n" );
document.write( "We could even define <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=A%2BB%2BC ALIGN=MIDDLE  ALT=\"N=A%2BB%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "The fact that C says<BR>\n" );
document.write( "\"It'd be better if B gave me two sweets. Then we'd all have the same amount!\"<BR>\n" );
document.write( "means <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B-2=C%2B2=A ALIGN=MIDDLE  ALT=\"B-2=C%2B2=A\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That is 3 equations, but not independent, so it is worth 2 equations.<BR>\n" );
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document.write( "The fact that B says<BR>\n" );
document.write( "\"If C gave me one sweet, I'd have twice as many as A does.\"<BR>\n" );
document.write( "means that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B%2B1=2A ALIGN=MIDDLE  ALT=\"B%2B1=2A\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "With that last equation, we have 3 independent equations, and that's enough to solve.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28A=B-2%2CA=C%2B2%2CB%2B1=2A%29 ALIGN=MIDDLE  ALT=\"system%28A=B-2%2CA=C%2B2%2CB%2B1=2A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We could even add <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=A%2BB%2BC ALIGN=MIDDLE  ALT=\"N=A%2BB%2BC\"   DISABLED_style= \"max-width:90%; height:auto;\" > and say we have a system of 4 linear equations, but why complicate when you can make it simpler.<BR>\n" );
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document.write( "Since two of the equations in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28A=B-2%2CA=C%2B2%2CB%2B1=2A%29 ALIGN=MIDDLE  ALT=\"system%28A=B-2%2CA=C%2B2%2CB%2B1=2A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > have only A and B, I can solve for A and B with just two equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28A=B-2%2CB%2B1=2A%29 ALIGN=MIDDLE  ALT=\"system%28A=B-2%2CB%2B1=2A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28A=B-2%2CB%2B1=2%28B-2%29%29 ALIGN=MIDDLE  ALT=\"system%28A=B-2%2CB%2B1=2%28B-2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28A=B-2%2CB%2B1=2B-4%29%29 ALIGN=MIDDLE  ALT=\"system%28A=B-2%2CB%2B1=2B-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28A=B-2%2CB%2B5=2B%29%29 ALIGN=MIDDLE  ALT=\"system%28A=B-2%2CB%2B5=2B%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28A=B-2%2C5=B%29%29 ALIGN=MIDDLE  ALT=\"system%28A=B-2%2C5=B%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28A=5-2%2Chighlight%28B=5%29%29%29 ALIGN=MIDDLE  ALT=\"system%28A=5-2%2Chighlight%28B=5%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28system%28A=3%2CB=5%29%29%29 ALIGN=MIDDLE  ALT=\"highlight%28system%28A=3%2CB=5%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now I can use the results above and the equation I have not used to find C.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28A=3%2CA=C%2B2%29 ALIGN=MIDDLE  ALT=\"system%28A=3%2CA=C%2B2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=C%2B2 ALIGN=MIDDLE  ALT=\"3=C%2B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3-2=C ALIGN=MIDDLE  ALT=\"3-2=C\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28C=1%29 ALIGN=MIDDLE  ALT=\"highlight%28C=1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Now, I can find the total<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC=3%2B5%2B1 ALIGN=MIDDLE  ALT=\"A%2BB%2BC=3%2B5%2B1\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%2BB%2BC=highlight%289%29 ALIGN=MIDDLE  ALT=\"A%2BB%2BC=highlight%289%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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