document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=850678>Question 850678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in.... </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #512301 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=512301\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use all rates as Jobs per Days.  Notice that C worker is given enough direct information for a rate value.  Start with the rate for C, and create rate equations for B & C, and for A & B.\r<BR>\n" );
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document.write( "Rate for C:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F50 ALIGN=MIDDLE  ALT=\"1%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" > jobs per day.\r<BR>\n" );
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document.write( "Let x = time for A to do 1 job.<BR>\n" );
document.write( "Let y = time for B to do 1 job.\r<BR>\n" );
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document.write( "First sentence tells, rate for A is equal to the combined rate of B and C.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2Fx=1%2Fy%2B1%2F50 ALIGN=MIDDLE  ALT=\"1%2Fx=1%2Fy%2B1%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "LCD is 50xy.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50%2Axy%2Fx=50%2Axy%2Fy%2B50%2Axy%2F50 ALIGN=MIDDLE  ALT=\"50%2Axy%2Fx=50%2Axy%2Fy%2B50%2Axy%2F50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50y=50x%2Bxy ALIGN=MIDDLE  ALT=\"50y=50x%2Bxy\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Second sentence tells, A and B together do the job in 10 days:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2Fx%2B1%2Fy%29=1%2F10 ALIGN=MIDDLE  ALT=\"%281%2Fx%2B1%2Fy%29=1%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "LCD is 10xy.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10xy%2Fx%2B10xy%2Fy=10xy%2F10 ALIGN=MIDDLE  ALT=\"10xy%2Fx%2B10xy%2Fy=10xy%2F10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10y%2B10x=xy ALIGN=MIDDLE  ALT=\"10y%2B10x=xy\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The system to solve for x and y is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50y=50x%2Bxy ALIGN=MIDDLE  ALT=\"50y=50x%2Bxy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10y%2B10x=xy ALIGN=MIDDLE  ALT=\"10y%2B10x=xy\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solving each of those for xy, and then equating each expression's formula for xy gives <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=50y-50x=10y%2B10x ALIGN=MIDDLE  ALT=\"50y-50x=10y%2B10x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplifying to <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2y=3x ALIGN=MIDDLE  ALT=\"2y=3x\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Solving the linear equation for a variable, trying y, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=3x%2F3 ALIGN=MIDDLE  ALT=\"y=3x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >;<BR>\n" );
document.write( "Picking either system equation, trying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10y%2B10x=xy ALIGN=MIDDLE  ALT=\"10y%2B10x=xy\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and substitute the expression for y found,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%2810%283x%2F2%29%2B10x=x%283x%2F2%29%29 ALIGN=MIDDLE  ALT=\"highlight_green%2810%283x%2F2%29%2B10x=x%283x%2F2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply left and right members by 2, and be sure to obtain this equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3x%5E2-50=0 ALIGN=MIDDLE  ALT=\"3x%5E2-50=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >  -----do not try to divide either sides by x thinking that to be simplification; it's a common beginners mistake.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight_green%28x%283x-50%29=0%29 ALIGN=MIDDLE  ALT=\"highlight_green%28x%283x-50%29=0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The meaningful answer for x is that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28x=50%2F3=16%262%2F3%29 ALIGN=MIDDLE  ALT=\"highlight%28x=50%2F3=16%262%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".. and use either system equation to find or solve for y.  You can also use the linear <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28y=%283%2F2%29x%29 ALIGN=MIDDLE  ALT=\"highlight%28y=%283%2F2%29x%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > found earlier. </SPAN>\n" );
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