document.write( "Question 883703: An ice cream vendor sells an average of 100 cones per day when the price of each cone is $10.00. The vendor believes that for each 50 – cents drop in the price, she will sell 20 more cones. What should the price of the cones be if she wants a revenue of $1440?
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Algebra.Com's Answer #533704 by josgarithmetic(39620)\"\" \"About 
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____y_________________x
\n" ); document.write( "Cones Sell__________Price
\n" ); document.write( "100_________________10.00
\n" ); document.write( "100+20_______________9.50
\n" ); document.write( "100+2*20____________10.00-2*0.50
\n" ); document.write( "100+3*20____________10.00-3*0.50\r
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\n" ); document.write( "\n" ); document.write( "The slope is \"m=-20%2F0.5=-40\".
\n" ); document.write( "A point known, as well as others, is (10,100).
\n" ); document.write( "y = How many cones sold.
\n" ); document.write( "\"y-100=-40%28x-10%29\" in point-slope form.
\n" ); document.write( "\"y-100=-40x%2B400\"
\n" ); document.write( "\"highlight_green%28y=-40x%2B500%29\".\r
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\n" ); document.write( "\n" ); document.write( "REVENUE: This is \"QuantitySold%2APrice\".
\n" ); document.write( "Quantity Sold = y
\n" ); document.write( "Price = x
\n" ); document.write( "Revenue is \"y%2Ax=%28-40x%2B500%29%2Ax\", but we are then really focusing on the function \"%28-40x%2B500%29%2Ax\" and want to equate this revenue expression (function) to $1440.\r
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\n" ); document.write( "\n" ); document.write( "\"highlight_green%28-40x%5E2%2B500x=1440%29\".
\n" ); document.write( "Simplify.
\n" ); document.write( "\"-4x%5E2%2B50x=144\"
\n" ); document.write( "\"-2x%5E2%2B25x-72=0\"
\n" ); document.write( "\"highlight_green%282x%5E2-25x%2B72=0%29\"\r
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\n" ); document.write( "\n" ); document.write( "Quadratic Formula Solution:
\n" ); document.write( "\"D=25%5E2-4%2A2%2A72=625-8%2A72=49\", the discriminant
\n" ); document.write( "\"x=%2825%2B-+7%29%2F4\"
\n" ); document.write( "\"x=18%2F4=9%2F2=highlight%284.5%29\"
\n" ); document.write( "OR
\n" ); document.write( "\"x=32%2F4=highlight%288.0%29\"
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\n" ); document.write( "Either of the two prices, $4.50 or $8.00 per cone would be expected to give the revenue 1440 dollars.
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