document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1005787>Question 1005787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this weighted average problem ; <BR>\n" );
document.write( "Your friends math test contained 42 questions some of which were worth 2 points , while the rest were worth 3 points.Your friend tells you that a perfect score is 100 points, but she cannot remember how many of each type were on the test . Help your friend out , how many of each type were on the test? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #621947 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=621947\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "x = number of 2 point questions<BR>\n" );
document.write( "y = number of 3 point questions\r<BR>\n" );
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document.write( "There are 42 questions total, so,<BR>\n" );
document.write( "x+y = 42\r<BR>\n" );
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document.write( "solve for y to get<BR>\n" );
document.write( "y = 42-x<BR>\n" );
document.write( "y = -x+42\r<BR>\n" );
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document.write( "There are x questions that are 2 points each. In total, we have 2x points just for these types of questions.\r<BR>\n" );
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document.write( "There are y questions that are 3 points each. In total, we have 3y points just for these types of questions.\r<BR>\n" );
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document.write( "The grand total is 2x+3y points. We're given the grand total to be 100.\r<BR>\n" );
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document.write( "So the second equation is 2x+3y = 100\r<BR>\n" );
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document.write( "Now we will replace the y in the second equation with -x+42 then solve for x\r<BR>\n" );
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document.write( "2x+3y = 100<BR>\n" );
document.write( "2x+3(-x+42) = 100<BR>\n" );
document.write( "2x-3x+126 = 100<BR>\n" );
document.write( "-x+126 = 100<BR>\n" );
document.write( "-x+126-126 = 100-126<BR>\n" );
document.write( "-x = -26<BR>\n" );
document.write( "x = 26\r<BR>\n" );
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document.write( "Use this x value to find the value of y\r<BR>\n" );
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document.write( "y = -x+42<BR>\n" );
document.write( "y = -26+42<BR>\n" );
document.write( "y = 16\r<BR>\n" );
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document.write( "Summary:<BR>\n" );
document.write( "x = 26 and y = 16\r<BR>\n" );
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document.write( "There are 26 two point questions and 16 three point questions. </SPAN>\n" );
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