document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=697541>Question 697541</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A group of friends planned a trip and chartered a bus for 300$. When 3 more friends decided to join the trip, the cost for the bus was $5 less per person. In all, how many people made the trip. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #430098 by </B><A HREF=/tutors/aboutme.mpl?userid=Stitch><B>Stitch(470)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Stitch><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=430098\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Set Up:<BR>\n" );
document.write( "Let A = the number of friends in the begining.<BR>\n" );
document.write( "Let B = the cost per person<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Equation 1: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+=+300%2FA ALIGN=MIDDLE  ALT=\"B+=+300%2FA\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+-+5+=+300%2F%28A+%2B+3%29 ALIGN=MIDDLE  ALT=\"B+-+5+=+300%2F%28A+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plug (300/A) into equation 2 for B<BR>\n" );
document.write( "Equation 2: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=B+-+5+=+300%2F%28A+%2B+3%29 ALIGN=MIDDLE  ALT=\"B+-+5+=+300%2F%28A+%2B+3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28300%2FA%29+-+5+=+300%2F%28A%2B3%29 ALIGN=MIDDLE  ALT=\"%28300%2FA%29+-+5+=+300%2F%28A%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "To simplify the equation, multiply both sides by (A+3)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28300%2FA%29%2A%28A%2B3%29+-+5%2A%28A%2B3%29+=+300 ALIGN=MIDDLE  ALT=\"%28300%2FA%29%2A%28A%2B3%29+-+5%2A%28A%2B3%29+=+300\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides by A<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300%2A%28A%2B3%29+-+5%2A%28A%2B3%29%2AA+=+300A ALIGN=MIDDLE  ALT=\"300%2A%28A%2B3%29+-+5%2A%28A%2B3%29%2AA+=+300A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300A+%2B+900+-+5A%2A%28A%2B3%29+=+300A ALIGN=MIDDLE  ALT=\"300A+%2B+900+-+5A%2A%28A%2B3%29+=+300A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Simplify<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=300A+%2B+900+-+5A%5E2+-+15A+=+300A ALIGN=MIDDLE  ALT=\"300A+%2B+900+-+5A%5E2+-+15A+=+300A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combine like terms<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=285A+%2B+900+-+5A%5E2+=+300A ALIGN=MIDDLE  ALT=\"285A+%2B+900+-+5A%5E2+=+300A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 285A from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900+-+5A%5E2+=+15A ALIGN=MIDDLE  ALT=\"900+-+5A%5E2+=+15A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Add 5A^2 to both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900+=+5A%5E2+%2B+15A ALIGN=MIDDLE  ALT=\"900+=+5A%5E2+%2B+15A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "*This step is not required but to make the numbers smaller pull a 5 from the right side of the equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=900+=+5%2A%28A%5E2+%2B+3A%29 ALIGN=MIDDLE  ALT=\"900+=+5%2A%28A%5E2+%2B+3A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Divide both sides by 5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=180+=+A%5E2+%2B+3A ALIGN=MIDDLE  ALT=\"180+=+A%5E2+%2B+3A\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Subtract 180 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+A%5E2+%2B+3A+-+180 ALIGN=MIDDLE  ALT=\"0+=+A%5E2+%2B+3A+-+180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Use the quadratic equation.<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
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=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=aA%5E2%2BbA%2Bc=0 ALIGN=MIDDLE  ALT=\"aA%5E2%2BbA%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1A%5E2%2B3A%2B-180+=+0 ALIGN=MIDDLE  ALT=\"1A%5E2%2B3A%2B-180+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"A%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%283%29%5E2-4%2A1%2A-180=729 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%283%29%5E2-4%2A1%2A-180=729\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=729 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28-3%2B-sqrt%28+729+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28-3%2B-sqrt%28+729+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B1%5D+=+%28-%283%29%2Bsqrt%28+729+%29%29%2F2%5C1+=+12 ALIGN=MIDDLE  ALT=\"A%5B1%5D+=+%28-%283%29%2Bsqrt%28+729+%29%29%2F2%5C1+=+12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5B2%5D+=+%28-%283%29-sqrt%28+729+%29%29%2F2%5C1+=+-15 ALIGN=MIDDLE  ALT=\"A%5B2%5D+=+%28-%283%29-sqrt%28+729+%29%29%2F2%5C1+=+-15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1A%5E2%2B3A%2B-180 ALIGN=MIDDLE  ALT=\"1A%5E2%2B3A%2B-180\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1A%5E2%2B3A%2B-180+=+1%28A-12%29%2A%28A--15%29 ALIGN=MIDDLE  ALT=\"1A%5E2%2B3A%2B-180+=+1%28A-12%29%2A%28A--15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 12, -15.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-180+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B3%2Ax%2B-180+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "\n" );
document.write( "Note that there are two answers; 12 & -15.<BR>\n" );
document.write( "Now we can not have negative people so your only answer is 12.<BR>\n" );
document.write( "That means that 12 people were the original group and then 3 more people joined.<BR>\n" );
document.write( "So there were 15 total people that made the trip.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );