document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=883807>Question 883807</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If i have a 67% in math what do i need to get on the eoct that is worth 20% of my grade to pass the class? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #534056 by </B><A HREF=/tutors/aboutme.mpl?userid=SmithWillSuffice><B>SmithWillSuffice(4)</B></A><img src=\"/images/stars/iconNewId_16x16.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=SmithWillSuffice><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=SmithWillSuffice><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=534056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a question about weighted averages.  In this case the \"weights\" are the proportions of the fimnal grade which are approtioned to each separate exam paper.  \r<BR>\n" );
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document.write( "Assuming they have no other exams to make up their grade, and assuming a \"pass\" means getting above 50% overall, then we can solve this puzzle using simple algebra and knowing how to compute averages.   We will also assume if EOCT is worth 20% of the overall grade, then the Maths score must be worth 80%.  So these will be the <b>weights</b> for the final computed average.  Weights do not always have to sum to =1, but if they are probabilities or percentages then they do need to sum to unity (otherwise it would imply you were missing something).<BR>\n" );
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document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+ ALIGN=MIDDLE  ALT=\"x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > be the minimum grade in the EOCT exam they need.  If we knew <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" > then their overall average grade would be,<BR>\n" );
document.write( "Overall  = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28+0.8%2A67+%2B++0.2%2Ax%29%2F%280.8%2B0.2%29.+ ALIGN=MIDDLE  ALT=\"+%28+0.8%2A67+%2B++0.2%2Ax%29%2F%280.8%2B0.2%29.+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Remember, for weighted averages we divide the weighted sum by the <i>sum of the weights</i>, not the number of items averaged.\r<BR>\n" );
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document.write( "Then we are simply being asked to solve for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+ ALIGN=MIDDLE  ALT=\"+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+=+%280.8%2A67+%2B++0.2%2Ax+%29%2F%281%29+ ALIGN=MIDDLE  ALT=\"+50+=+%280.8%2A67+%2B++0.2%2Ax+%29%2F%281%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+=+0.8%2A67+%2B++0.2%2A+x+ ALIGN=MIDDLE  ALT=\"+50+=+0.8%2A67+%2B++0.2%2A+x+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+=+%288%29%2F%2810%29+%2A+67+%2B++%282%29%2F%2810%29+%2A+x++ ALIGN=MIDDLE  ALT=\"+50+=+%288%29%2F%2810%29+%2A+67+%2B++%282%29%2F%2810%29+%2A+x++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+50+=+536%2F10+%2B++%282%29%2F%2810%29+%2A+x++ ALIGN=MIDDLE  ALT=\"+50+=+536%2F10+%2B++%282%29%2F%2810%29+%2A+x++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%29%2F%2810%29+%2A+x+=+50+-++%28536%29%2F%2810%29++ ALIGN=MIDDLE  ALT=\"+%282%29%2F%2810%29+%2A+x+=+50+-++%28536%29%2F%2810%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%282%29%2F%2810%29+%2A+x+=+%28500+-+536%29%2F%2810%29++ ALIGN=MIDDLE  ALT=\"+%282%29%2F%2810%29+%2A+x+=+%28500+-+536%29%2F%2810%29++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=++2%2Ax+=+500+-+536++ ALIGN=MIDDLE  ALT=\"++2%2Ax+=+500+-+536++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+2%2Ax+=+-36+ ALIGN=MIDDLE  ALT=\"+2%2Ax+=+-36+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-%2836%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"+x+=+-%2836%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "thus <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x+=+-18.+ ALIGN=MIDDLE  ALT=\"+x+=+-18.+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "That's the answer, believe it or not!<BR>\n" );
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document.write( "What does it mean?  It means you can afford a negative score on the final exam.  Since placing your name on the exam paper will win you a score of 0\% at least, this is all you need.  You cannot fail provided you turn up to hand in the EOCT  exam paper.  :-)\r<BR>\n" );
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document.write( "<b>Reflect:</b>  If you don't believe that st answer, just imagine you do only get 0% on the EOCT exam.  Then what is your final grade?  \r<BR>\n" );
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document.write( "<b>Answer:</b> It will be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%280.8+%2A+67+%2B+0+%2A+0.2+%29%2F%280.8%2B0.2%29+=+53.6+ ALIGN=MIDDLE  ALT=\"+%280.8+%2A+67+%2B+0+%2A+0.2+%29%2F%280.8%2B0.2%29+=+53.6+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which is a pass. </SPAN>\n" );
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