document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=803073>Question 803073</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of 100 people, some students and some faculty, attended a museum opening. Each student paid $10 per person for entrance to the museum and each of the faculty paid $25 per person for entrance.  If the total paid, for all 100 people, was $1300, how many students attended the museum opening? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #484112 by </B><A HREF=/tutors/aboutme.mpl?userid=homeworkhedgehog><B>homeworkhedgehog(9)</B></A><img src=\"/images/stars/stars-05.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=homeworkhedgehog><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=homeworkhedgehog><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=484112\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This is a system of equations problem, meaning that you need two equations to solve for two variables (number of students, number of faculty).\r<BR>\n" );
document.write( "\n" );
document.write( "The situation is $10 x (the number of students) + $25 x (the number of faculty) = $1300 total\r<BR>\n" );
document.write( "\n" );
document.write( "If we use variables, we get\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10s+%2B+25f+=+1300 ALIGN=MIDDLE  ALT=\"10s+%2B+25f+=+1300\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The other equation we need is a bit simpler but a little more hidden in the question:\r<BR>\n" );
document.write( "\n" );
document.write( "There are only two types of people (students, faculty) attending and we know the total is 100, so our equation is \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+%2B+f+=+100 ALIGN=MIDDLE  ALT=\"s+%2B+f+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "From here, we can use Elimination or Substitution to solve for the number of students, s.\r<BR>\n" );
document.write( "\n" );
document.write( "We'll use substitution:\r<BR>\n" );
document.write( "\n" );
document.write( "If we solve \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+%2B+f+=+100 ALIGN=MIDDLE  ALT=\"s+%2B+f+=+100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "for f by subtracting s from both sides, we get\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=f+=+100+-+s ALIGN=MIDDLE  ALT=\"f+=+100+-+s\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Now we can plug f back into the other equation and solve for s:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10s+%2B+25%28100+-+s%29+=+1300 ALIGN=MIDDLE  ALT=\"10s+%2B+25%28100+-+s%29+=+1300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10s+%2B+2500+-+25s+=+1300 ALIGN=MIDDLE  ALT=\"10s+%2B+2500+-+25s+=+1300\"   DISABLED_style= \"max-width:90%; height:auto;\" >  ;  Distribute 25<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15s+%2B+2500+=+1300 ALIGN=MIDDLE  ALT=\"-15s+%2B+2500+=+1300\"   DISABLED_style= \"max-width:90%; height:auto;\" >          ;  Combine \"like\" terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-15s+=+-1200 ALIGN=MIDDLE  ALT=\"-15s+=+-1200\"   DISABLED_style= \"max-width:90%; height:auto;\" >                    ;  Subtract 2500 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+80 ALIGN=MIDDLE  ALT=\"s+=+80\"   DISABLED_style= \"max-width:90%; height:auto;\" >                                ;  Divide both sides by -15\r<BR>\n" );
document.write( "\n" );
document.write( "So we find out that there are 80 students. \r<BR>\n" );
document.write( "\n" );
document.write( "You can check your answers by realizing that since there are 80 students out of 100, the other 20 must be faculty. \r<BR>\n" );
document.write( "\n" );
document.write( "Plug s = 80 and f = 20 into your original equation of\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10s+%2B+25f+=+1300 ALIGN=MIDDLE  ALT=\"10s+%2B+25f+=+1300\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "to get\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10%2880%29+%2B+25%2820%29 ALIGN=MIDDLE  ALT=\"10%2880%29+%2B+25%2820%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=800+%2B+500%29 ALIGN=MIDDLE  ALT=\"800+%2B+500%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1300 ALIGN=MIDDLE  ALT=\"1300\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "And it checks out. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );