document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=124214>Question 124214</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A TEST IS WORTH 150 PTS. THERE ARE 46 3 AND 5 PT QUESTIONS.  HOW MANY OF EACH IS 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 #91072 by </B><A HREF=/tutors/aboutme.mpl?userid=edjones><B>edjones(8007)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=edjones><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=edjones><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=91072\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let t be the number of 3 pt queations.<BR>\n" );
document.write( "Let f be the number of 5 pt queations.<BR>\n" );
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document.write( "t+f=46<BR>\n" );
document.write( "3t+5f=150<BR>\n" );
document.write( ".<BR>\n" );
document.write( "40 three point questions and 6 five pointers.<BR>\n" );
document.write( "Ed<BR>\n" );
document.write( ".<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=change_this_name6744.solver>Linear Systems by Addition</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>We'll solve the system:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2At+%2B+1%2Af+=+46 ALIGN=MIDDLE  ALT=\"1%2At+%2B+1%2Af+=+46\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2At+%2B+5%2Af+=+150 ALIGN=MIDDLE  ALT=\"3%2At+%2B+5%2Af+=+150\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  by elimination by addition.To eliminate by addition, we need to set both coefficients of x to numbers with changed signs, i.e a and -a. Since in the second equation we have 3 as our coefficient for x, to get  -1 we have to multiply all terms of the second equation by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2F3 ALIGN=MIDDLE  ALT=\"-1%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is equal to -0.333333333333333.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Multiplying, we get on our second equation:<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%2A-0.333333333333333%29t+%2B+%285%2A-0.333333333333333%29f+=+150%2A-0.333333333333333 ALIGN=MIDDLE  ALT=\"%283%2A-0.333333333333333%29t+%2B+%285%2A-0.333333333333333%29f+=+150%2A-0.333333333333333\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-1%2At+%2B+-1.66666666666667%2Af+=+-50 ALIGN=MIDDLE  ALT=\"-1%2At+%2B+-1.66666666666667%2Af+=+-50\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Adding both equations we get:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2B-1%29t+%2B+%281%2B-1.66666666666667%29f+=+%2846%2B-50%29 ALIGN=MIDDLE  ALT=\"%281%2B-1%29t+%2B+%281%2B-1.66666666666667%29f+=+%2846%2B-50%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Since 1 and -1 cancel out, we have a linear equation:Therefore, we know that f = 6.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Plugging that in into the first equation gives us:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2At+%2B+1%2Af+=+46 ALIGN=MIDDLE  ALT=\"1%2At+%2B+1%2Af+=+46\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2At+%2B+1%2A6+=+46 ALIGN=MIDDLE  ALT=\"1%2At+%2B+1%2A6+=+46\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2At+%2B+6+=+46 ALIGN=MIDDLE  ALT=\"1%2At+%2B+6+=+46\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2At+=+46+-+6 ALIGN=MIDDLE  ALT=\"1%2At+=+46+-+6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+%2846+-+6%29%2F1 ALIGN=MIDDLE  ALT=\"t+=+%2846+-+6%29%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+40%2F1 ALIGN=MIDDLE  ALT=\"t+=+40%2F1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t+=+40 ALIGN=MIDDLE  ALT=\"t+=+40\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Therefore, our answer is:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=system%28+t=40%2C+f=6+%29 ALIGN=MIDDLE  ALT=\"system%28+t=40%2C+f=6+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
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document.write( " </SPAN>\n" );
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