document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=24137>Question 24137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> your teacher is giving you a test worth 100 points containing 40 questions.  there are two point and four point questions on the test.  how many of each type of question are 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 #12825 by </B><A HREF=/tutors/aboutme.mpl?userid=kev82><B>kev82(151)</B></A><img src=\"/images/stars/stars-09.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=kev82><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=12825\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <p>We're trying to find out how many two point questions, and how many four point questions there are. So it's probably a good choice to choose these as our variables. Let's call the the number of two point questions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the number of four point questions <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f ALIGN=MIDDLE  ALT=\"f\"   DISABLED_style= \"max-width:90%; height:auto;\" >.</p>\r<BR>\n" );
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document.write( "<p>Now let's look at the information we've been given by the problem.<p>\r<BR>\n" );
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document.write( "<blockquote>worth 100 points</blockquote>\r<BR>\n" );
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document.write( "<p>So twice the number of two point questions, plus four times the number of four point questions equals 100.</p>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2t%2B4f=100 ALIGN=MIDDLE  ALT=\"2t%2B4f=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<blockquote>containing 40 questions</blockquote>\r<BR>\n" );
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document.write( "<p>So the number of two point questions, plus the number of four point questions equals 40.</p>\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t%2Bf=40 ALIGN=MIDDLE  ALT=\"t%2Bf=40\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<p>Using the super duper 2x2 linear simultaneous equation solver, this is my first time using it btw. We get:</p>\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=linear.solver>Linear System solver (using determinant)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Solve:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++2%5Ct+%2B+4%5Cf+=+100%2C%0D%0A++++1%5Ct+%2B+1%5Cf+=+40+%29%0D%0A++ ALIGN=MIDDLE  ALT=\"+system%28+%0D%0A++++2%5Ct+%2B+4%5Cf+=+100%2C%0D%0A++++1%5Ct+%2B+1%5Cf+=+40+%29%0D%0A++\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Any system of equations:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++a%5B11%5D%2At+%2B+a%5B12%5D%2Af+=+b%5B1%5D%2C%0D%0A++++a%5B21%5D%2At+%2B+a%5B22%5D%2Af+=+b%5B2%5D%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  has solution<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++t+=+%28b%5B1%5D%2Aa%5B22%5D+-+b%5B2%5D%2Aa%5B12%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%2C%0D%0A++++f+=+%28a%5B11%5D%2Ab%5B2%5D+-+a%5B21%5D%2Ab%5B1%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  or<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+system%28+%0D%0A++++++t+=+%28100%2A1+-+40%2A4%29%2F%282%2A1-1%2A4%29+=+30%2C%0D%0A++++++f+=+%282%2A40+-+1%2A100%29%2F%282%2A1-1%2A4%29+=+10%0D%0A++++%29%0D%0A++ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  (t=30, f=10}<BR>\n" );
document.write( "  </TD></TR>\n" );
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document.write( "<p>Always remember to substitute in and check the answer is right.</p>\r<BR>\n" );
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document.write( "<p>Hope that helps</p>\r<BR>\n" );
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document.write( "<p>Kev</p> </SPAN>\n" );
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