document.write( "Question 887775: A bus company has 3,000 passengers daily, paying a $1.25 fare. For each 25¢ increase in fare, the company estimate that it will lose 80 passengers. What is the smallest increase in fare that will produce a $4,970 daily revenue\r
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Algebra.Com's Answer #537611 by Edwin McCravy(20054) $\"\"$ $\"About$

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A bus company has 3,000 passengers daily, paying a $1.25 fare. For each 25¢ increase in fare, the company estimate that it will lose 80 passengers. What is the smallest increase in fare that will produce a $4,970 daily revenue
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document.write( "Let x = the smallest number of 25¢ increases in the fare that will produce \r\n" );
document.write( "the $4970 daily revenue.\r\n" );
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document.write( "Then the new fare is $1.25 + $0.25x or 1.25 + 0.25x\r\n" );
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document.write( "For each of the x 25¢ increase in fare, the company will lose 80\r\n" );
document.write( "passengers\r\n" );
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document.write( "Then the new number of passengers will be 3000 - 80x\r\n" );
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document.write( "Therefore the new daily revenue will be (3000 - 80x)(1.25 + 0.25x)\r\n" );
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document.write( "This must equal to $4970. So the equation is \r\n" );
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document.write( "               (3000 - 80x)(1.25 + 0.25x) = 4970\r\n" );
document.write( "Use FOIL:\r\n" );
document.write( "               3750 + 750x - 100x - 20x² = 4970\r\n" );
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document.write( "                     -20x² + 650x - 1220 = 0\r\n" );
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document.write( "Divide thru by -10       2x² - 65x + 122 = 0\r\n" );
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document.write( "Factor:                     (2x-61)(x-2) = 0\r\n" );
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document.write( "                        2x-61=0;   x-2=0\r\n" );
document.write( "                           2x=61;    x=2\r\n" );
document.write( "                            x=30.5;  \r\n" );
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document.write( "The answer 30.5 makes no sense.  The only answer that makes sense is \r\n" );
document.write( "x = 2.  That is, 2 25¢ increases will bring in the desired revenue.\r\n" );
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document.write( "Checking:  The new fare will be $1.75. There will be 2×80 = 160 passengers\r\n" );
document.write( "lost.  So there will be 3000-160 passengers or 2840 passengers, each paying\r\n" );
document.write( "$1.75 so the total revenue will be 2840×$1.75 or $4970.  So the answer is\r\n" );
document.write( "correct.\r\n" );
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document.write( "Edwin

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