document.write( "Question 666312: A motel advertises that it will provide dinner, dancing, and drinks for $60 per couple at a New Year's Eve party. It must have a guarantee of 50 couples. Furthermore, it will agree that for each couple in excess of 50, it will reduce the price per couple for all attending by $0.25. How many couples will it take to maximize the motel's revenue?
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Algebra.Com's Answer #415460 by lwsshak3(11628)\"\" \"About 
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A motel advertises that it will provide dinner, dancing, and drinks for $60 per couple at a New Year's Eve party. It must have a guarantee of 50 couples. Furthermore, it will agree that for each couple in excess of 50, it will reduce the price per couple for all attending by $0.25. How many couples will it take to maximize the motel's revenue?
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\n" ); document.write( "let x=number of couples to maximize motel's revenue
\n" ); document.write( "x-50=number of couples in excess of 50
\n" ); document.write( ".25(x-50)=reduction in price per couple
\n" ); document.write( "Price per couple=[60-.25(x-50)]
\n" ); document.write( "Revenue=number of couples*price per couple
\n" ); document.write( "y=x[60-(.25(x-50)]
\n" ); document.write( "=x[60-.25x+12.5]
\n" ); document.write( "=x[-.25x+72.5]
\n" ); document.write( "=-.25x^2+72.5x
\n" ); document.write( "complete the square
\n" ); document.write( "y=-.25(x^2-290+145^2)+.25*145^2
\n" ); document.write( "y=-.25(x-145)^2+5256.25
\n" ); document.write( "This is a parabola that opens downwards with a maximum of 5256.25 at x=145
\n" ); document.write( "How many couples will it take to maximize the motel's revenue=145 \r
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