document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187922>Question 1187922</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A banquet hall charges a rental fee plus an additional charge for each guest. The total cost is $550 for 20 guests and $775 for 35 guests. <BR>\n" );
document.write( "Find an equation to model the total cost, C, in terms of the number of guests, N. </SPAN>\n" );
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document.write( "Informally....<br><BR>\n" );
document.write( "The additional 35-20=15 guests cost an additional $775-$550=$225, so the cost per guest is $225/15 = $15.<br><BR>\n" );
document.write( "Since the cost for 20 guests is $550, the rental fee is $550-20($15)=$550-$300=$250.<br><BR>\n" );
document.write( "So the rental cost is a fee of $250 plus $15 per guest.<br><BR>\n" );
document.write( "Using formal algebra -- note that the calculations performed are exactly the same....<br><BR>\n" );
document.write( "(x(1),y(1))=(20,550)<BR>\n" );
document.write( "(x(2),y(2))=(35,775)<br><BR>\n" );
document.write( "The slope m (increase in cost (y) per guest (x)) is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=m+=+%28y%282%29-y%281%29%29%2F%28x%282%29-x%281%29%29+=+%28775-550%29%2F%2835-20%29+=+225%2F15+=+15 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The equation is of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=mx%2Bb ALIGN=MIDDLE  ALT=\"y=mx%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" >; and we know the slope m is 15.  Plug in (x,y) = (20,550) to find b.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=550+=+15%2820%29%2Bb ALIGN=MIDDLE  ALT=\"550+=+15%2820%29%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=550+=+300%2Bb ALIGN=MIDDLE  ALT=\"550+=+300%2Bb\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=250 ALIGN=MIDDLE  ALT=\"b=250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER: The equation for the total cost C for N guests is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C=15N%2B250 ALIGN=MIDDLE  ALT=\"C=15N%2B250\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );