document.write( "Question 447845: The total number of seats in a basketball sports arena is 12,000. The arena is divided into three sections, court sides, end zone and balcony, and there are twice as many balcony seats as court side seats. For the conference championship game, ticket price were $10.00 for court side, $8.00 for balcony and $7.00 for end-zone. If the arena was sold out for the game and the total receipts were $99,000 how many seats were court-side???.... thank you ^^ \n" ); document.write( "

Algebra.Com's Answer #853349 by ikleyn(53560) $\"\"$ $\"About$

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\n" ); document.write( "The total number of seats in a basketball sports arena is 12,000. The arena is divided into three sections,
\n" ); document.write( "court sides, end zone and balcony, and there are twice as many balcony seats as court side seats.
\n" ); document.write( "For the conference championship game, ticket price were $10.00 for court side, $8.00 for balcony
\n" ); document.write( "and $7.00 for end-zone. If the arena was sold out for the game and the total receipts were $99,000
\n" ); document.write( "how many seats were court-side?
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\n" ); document.write( "\n" ); document.write( "        Two other solutions to this problem at this forum do introduce a system of three equations for\r
\n" ); document.write( "\n" ); document.write( "        three unknown. Then they make many transformations and pronounce many words to solve \r
\n" ); document.write( "\n" ); document.write( "        this system of equations, demonstrating great diligence and stupidity.\r
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\n" ); document.write( "\n" ); document.write( "        There is another, more elegant, straightforward and effective way to solve this problem \r
\n" ); document.write( "\n" ); document.write( "        using only one equation and one unknown.\r
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document.write( "Let x be the number of the courtside seats.\r\n" );
document.write( "Then the number of the balcony seats is 2x\r\n" );
document.write( "and the number of the zone seats is (12000-x-2x) = (12000-3x).\r\n" );
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document.write( "Write the equation for the total money\r\n" );
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document.write( "    10x + 8*(2x) + 7*(12000-3x) = 99000  dollars.\r\n" );
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document.write( "Simplify this equation and find x\r\n" );
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document.write( "    10x + 16x + 84000 - 21x = 99000,\r\n" );
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document.write( "    10x + 16x - 21x = 99000 - 84000,\r\n" );
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document.write( "            5x      =     15000,\r\n" );
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document.write( "             x      =      15000/5 = 3000.\r\n" );
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document.write( "So, the number of the court-side seats was 3000.     ANSWER\r\n" );
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