document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=935100>Question 935100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There are 20 true/false questions and 20 multiple choice questions on a test.\r<BR>\n" );
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document.write( "A correct answer to a true false question earns 10 points. \r<BR>\n" );
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document.write( "A correct answer to a multiple choice question earns 12 points.\r<BR>\n" );
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document.write( "The test makers determined that it takes, on average 3 minutes to answer a true/false question and 4 minutes to answer a multiple choice question. Students have 1 hour to answer to answer at most 18 questions of their choice. How many of each kind of question should a student answer correctly to get the greatest possible score?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #568246 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=568246\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There are 20 true/false questions and 20 multiple choice questions on a test.<BR>\n" );
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document.write( "A correct answer to a true false question earns 10 points. <BR>\n" );
document.write( "A correct answer to a multiple choice question earns 12 points.<BR>\n" );
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document.write( "The test makers determined that it takes, on average 3 minutes to answer a true/false question and 4 minutes to answer a multiple choice question.<BR>\n" );
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document.write( "Students have 1 hour to answer at most 18 questions of their choice. How many of each kind of question should a student answer correctly to get the greatest possible score?<BR>\n" );
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document.write( "t + m <= 18 questions<BR>\n" );
document.write( "3t + 4m <= 60 minutes<BR>\n" );
document.write( "Objective Rule:: Score = 10t + 12m<BR>\n" );
document.write( "t >= 0<BR>\n" );
document.write( "m >= 0<BR>\n" );
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document.write( "Graph::<BR>\n" );
document.write( "t = -m + 18 and shade the area below it in QI<BR>\n" );
document.write( "t = (-4/3)m + 20 and shade the area below it in QI<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28400%2C400%2C-5%2C40%2C-5%2C30%2C-x%2B18%2C%28-4%2F3%29x%2B20%29 ALIGN=MIDDLE  ALT=\"graph%28400%2C400%2C-5%2C40%2C-5%2C30%2C-x%2B18%2C%28-4%2F3%29x%2B20%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Find the intercepts and the intersection of the 2 lines.<BR>\n" );
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document.write( "(0,18) and (18,0) for t = -m+18<BR>\n" );
document.write( "(0,20) and (15,0) for t = (-4/3)m+20<BR>\n" );
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document.write( "Find the intersection of the 2 lines:<BR>\n" );
document.write( "-m+18 = (-4/3)m + 20<BR>\n" );
document.write( "(1/3)m = 2<BR>\n" );
document.write( "m = 6 ; and t = -m+18, so t = 12<BR>\n" );
document.write( "Intersection:: (6,12)<BR>\n" );
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document.write( "Substitute the proper point coordinates into the Objective Function<BR>\n" );
document.write( "to determine which combination of t(true/false) and m(multiple choice)<BR>\n" );
document.write( "gives a maximum value.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( " </SPAN>\n" );
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