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A bus company has 4000 passengers daily, each paying a fare of $2. For each $.015 increase, the company estimates that it will lose 40 passengers per day. If the company needs to take in $10,450 per day to stay in business, what fare should be charged?
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\n" ); document.write( "Let x = no. of .15 fare increases to attain a revenue of $10,450
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\n" ); document.write( "No. of passengers: (4000-40x)
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\n" ); document.write( "Fare charged: (2+.15x)
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\n" ); document.write( "The equation:
\n" ); document.write( "No. of pass * fare charge = $10450
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\n" ); document.write( "(4000 - 40x) * (2 + .15x) = 10450
\n" ); document.write( "FOIL
\n" ); document.write( "8000 + 600x - 80x - 6x^2 = 10450
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\n" ); document.write( "Arrange as a quadratic equation
\n" ); document.write( "-6x^2 + 520x + 8000 - 10450 = 0
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\n" ); document.write( "-6x^2 + 520x - 2450 = 0
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\n" ); document.write( "Simplify, divide equation by -2
\n" ); document.write( "+3x^2 - 260x + 1225 = 0
\n" ); document.write( "Factor this to:
\n" ); document.write( "(3x - 245) (x - 5) = 0
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\n" ); document.write( "x = +5 is the only reasonable solution
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\n" ); document.write( "That means five .15 increases
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\n" ); document.write( "5 * .15 = .75 increase above $2 = $2.75
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\n" ); document.write( "We can check this: 5 * 40 = 200 decrease in passengers, from 4000
\n" ); document.write( "3800 * 2.75 = 10450 \n" ); document.write( "