document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1019503>Question 1019503</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A college charters a bus for $1500 to take a group of students to see a Broadway production. When 10 more students join the trip, the cost per student decreases by $12.50. How many students were in the original group?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #635451 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=635451\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A college charters a bus for $1500 to take a group of students to see a Broadway production.<BR>\n" );
document.write( " When 10 more students join the trip, the cost per student decreases by $12.50.<BR>\n" );
document.write( " How many students were in the original group?<BR>\n" );
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document.write( "let x = the original no. of students<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(x+10) = the actual no. that went on the trip<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500%2Fx ALIGN=MIDDLE  ALT=\"1500%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the original cost per student<BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500%2F%28%28x%2B10%29%29 ALIGN=MIDDLE  ALT=\"1500%2F%28%28x%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the actual cost <BR>\n" );
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document.write( "Original cost  - actual cost = $12.50<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500%2Fx ALIGN=MIDDLE  ALT=\"1500%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500%2F%28%28x%2B10%29%29 ALIGN=MIDDLE  ALT=\"1500%2F%28%28x%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 12.50<BR>\n" );
document.write( "multiply equation by x(x+10)<BR>\n" );
document.write( "x(x+10)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500%2Fx ALIGN=MIDDLE  ALT=\"1500%2Fx\"   DISABLED_style= \"max-width:90%; height:auto;\" > - x(x+10)*<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1500%2F%28%28x%2B10%29%29 ALIGN=MIDDLE  ALT=\"1500%2F%28%28x%2B10%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 12.50x(x+10)<BR>\n" );
document.write( "Cancel the denominators<BR>\n" );
document.write( "1500(x+10) - 1500x = 12.5x(x+10)<BR>\n" );
document.write( "1500x + 15000 - 1500x = 12.5x^2 + 125x<BR>\n" );
document.write( "Combine on the right to form a quadratic equation<BR>\n" );
document.write( "0 = 12.5x^2 + 125x - 15000<BR>\n" );
document.write( "Simplify, divide equation by 12.5<BR>\n" );
document.write( "x^2 + 10x - 1200 = 0<BR>\n" );
document.write( "You can use the quadratic formula; a=1; b=10; c=-1200, but this will factor to<BR>\n" );
document.write( "(x + 40(x - 30) = 0<BR>\n" );
document.write( "The positive solution is what we want here<BR>\n" );
document.write( "x = 30 students in the original group<BR>\n" );
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document.write( "Check this by finding the cost per student for each scenario<BR>\n" );
document.write( "1500/30 = $50.00; original cost<BR>\n" );
document.write( "1500/40 = $37.50; actual cost<BR>\n" );
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document.write( "saving:  $12.50<BR>\n" );
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