document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252699>Question 252699</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A caterer charges a fixed cost for preparing dinner plus an additional cost for each person served. You know the cost for 100 students will be $750 and the cost for 150 students will be $1050. Find the caterer's fixed cost and the cost per student served. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184731 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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=184731\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let the cost function be:<BR>\n" );
document.write( "(i) C = mP + b<BR>\n" );
document.write( "Where C = total cost, P = number of people, b = fixed cost, and m = cost per person.<BR>\n" );
document.write( "we actually have coordinates: (100,750) and (150,1050). We put those into (i).<BR>\n" );
document.write( "(ii) 750 = 100m + b<BR>\n" );
document.write( "(iii) 1050 = 150m + b.<BR>\n" );
document.write( "At this point, multiply (ii) by -1 and add down.<BR>\n" );
document.write( "(iv) 300 = 50m<BR>\n" );
document.write( "m = 6: Cost per student<BR>\n" );
document.write( "Now we put 6 back into (ii) for m to find b.<BR>\n" );
document.write( "(v) 750 = 100(6) + b<BR>\n" );
document.write( "b = 150: fixed cost<BR>\n" );
document.write( "C = 6P + 150. </SPAN>\n" );
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