document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1101815>Question 1101815</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi\r<BR>\n" );
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document.write( "3 identical basins, A, B, C were filled with water. Basin A had a mass of 3.1kg when it was half full.<BR>\n" );
document.write( "Basin B had a mass of 2.2kg when it was 1/5 full. What fraction of basin C was filled with water when it hsd a mass of 2.8kg.\r<BR>\n" );
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document.write( "thanks </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #716497 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=716497\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The other tutor started on a solution but did not finish it.  While her method seems a bit unusual to me, it is valid; I assume she just did not see how to finish it.<br><BR>\n" );
document.write( "I will finish her solution and then show my very different solution.<br><BR>\n" );
document.write( "She got to the point where she had the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+%28x%2F3%29-+%288%2F15%29 ALIGN=MIDDLE  ALT=\"y+=+%28x%2F3%29-+%288%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "where y is the fraction of the basin that is filled and x is the total mass of the basin and water.<br><BR>\n" );
document.write( "To continue solving the problem by this process, we can solve the equation for x when y=0 to give us the mass of the basin alone, and then solve the equation for x when y=1 to give us the total mass of the basin and the water.<br><BR>\n" );
document.write( "mass of basin alone; y = 0:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+%28x%2F3%29+-+%288%2F15%29 ALIGN=MIDDLE  ALT=\"0+=+%28x%2F3%29+-+%288%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2F3%29+=+%288%2F15%29 ALIGN=MIDDLE  ALT=\"%28x%2F3%29+=+%288%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+24%2F15+=+1.6 ALIGN=MIDDLE  ALT=\"x+=+24%2F15+=+1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "mass of basin and water when basin is full; y = 1:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+=+%28x%2F3%29+-+%288%2F15%29 ALIGN=MIDDLE  ALT=\"1+=+%28x%2F3%29+-+%288%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=23%2F15+=+x%2F3 ALIGN=MIDDLE  ALT=\"23%2F15+=+x%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+23%2F5+=+4.6 ALIGN=MIDDLE  ALT=\"x+=+23%2F5+=+4.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So the basin empty has a mass of 1.6kg; full it has a mass of 4.6kg; so the mass of the water is 3kg.<br><BR>\n" );
document.write( "So if basin C had a mass of 2.8kg, the mass of water it contained was 1.2kg; the fraction that basin C is full is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.2%2F3+=+2%2F5 ALIGN=MIDDLE  ALT=\"1.2%2F3+=+2%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Now for a very different solution....<br><BR>\n" );
document.write( "This shows you how very different the amount of work required to solve a problem can be, depending on how you define the variables in the problem.<br><BR>\n" );
document.write( "And the lesson from that is that you should never be afraid to try solving a problem by a different method than everybody else -- you might find a better method.<BR>\n" );
document.write( "That's how progress is made in the world of science and mathematics.<br><BR>\n" );
document.write( "So here is my setup for the problem:<br><BR>\n" );
document.write( "Let x be the mass of each basin<BR>\n" );
document.write( "Let y be the mass of water in a full basin<br><BR>\n" );
document.write( "Basin A has a mass of 3.1kg when half full:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+.5y+=+3.1 ALIGN=MIDDLE  ALT=\"x+%2B+.5y+=+3.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Basin B has a mass of 2.2kg when one-fifth full:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+.2y+=+2.2 ALIGN=MIDDLE  ALT=\"x+%2B+.2y+=+2.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Subtract the two equations:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.3y+=+.9 ALIGN=MIDDLE  ALT=\".3y+=+.9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+3 ALIGN=MIDDLE  ALT=\"y+=+3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Substitute into either equation:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+%2B+.5%283%29+=+3.1 ALIGN=MIDDLE  ALT=\"x+%2B+.5%283%29+=+3.1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+1.6 ALIGN=MIDDLE  ALT=\"x+=+1.6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Each basin has a mass of 1.6kg; the mass of water in a full basin is 3kg.<br><BR>\n" );
document.write( "Now we are at the same point we were in the other solution; we finish as before, finding that basin C is 2/5 full if it has a mass of 2.8kg. </SPAN>\n" );
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