document.write( "Question 887660: When the admission price to a game is £0.50, 10,000 people attend. For every increase of £0.05 in the admission price, 200 fewer people attend. Find the admission price that yields the largest income. What is the largest income?
\n" ); document.write( " Many thanks in advance for your help. \n" ); document.write( "
Algebra.Com's Answer #536848 by ankor@dixie-net.com(22740)\"\" \"About 
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When the admission price to a game is £0.50, 10,000 people attend.
\n" ); document.write( " For every increase of £0.05 in the admission price, 200 fewer people attend.
\n" ); document.write( " Find the admission price that yields the largest income.
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\n" ); document.write( "let x = no. of 5 cent increases, also = the multiple of 200 people decreases
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\n" ); document.write( "Income = price * no. of people
\n" ); document.write( "I = (.50+.05x)(10000-200x)
\n" ); document.write( "FOIL
\n" ); document.write( "I = 5000 - 100x + 500x - 10x^2
\n" ); document.write( "Combine to form a quadratic equation
\n" ); document.write( "I = -10x^2 + 400x + 5000
\n" ); document.write( "simplify divide by 10
\n" ); document.write( "I = -x^2 + 40x + 500
\n" ); document.write( "The min will occur at the axis of symmetry, x = -b(2a)
\n" ); document.write( "x = \"%28-40%29%2F%282%2A-1%29\"
\n" ); document.write( "x = 20 five cent increases
\n" ); document.write( "therefore
\n" ); document.write( "1.50 is the increased price
\n" ); document.write( "and
\n" ); document.write( "10000 -(20*200) = 6000 people
\n" ); document.write( "\"What is the largest income? \"
\n" ); document.write( "$1.50 * 6000 = $9000 is the max income
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