document.write( "Question 1100563: A stadium has 50,000 seats. Seats sell for $25 in section A, $20 in section B, $15 in section C. The number of seats in section A equals the total number of seats in sections B and C. Suppose the stadium takes in 1,074,500 from each sold-out event. How many seats does each section holds? \n" ); document.write( "

Algebra.Com's Answer #715101 by ikleyn(52835) $\"\"$ $\"About$

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.A stadium has 50,000 seats. Seats sell for $25 in section A, $20 in section B, $15 in section C.
\n" ); document.write( "The number of seats in section A equals the total number of seats in sections B and C.
\n" ); document.write( "Suppose the stadium takes in 1,074,500 from each sold-out event. How many seats does each section holds?
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document.write( "Let x be the number of seats in section B, and y be the number of seats in section C.\r\n" );
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document.write( "Then the number of seats in section A is x+y, the sum of seats in sections B and C, according to the condition.\r\n" );
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document.write( "The condition says\r\n" );
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document.write( "seatsA + seatsB + seatsC = 50000,   or\r\n" );
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document.write( "(x+y)  + x      + y      = 50000,   which is the same as\r\n" );
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document.write( "2(x+y) = 50000,                     which implies\r\n" );
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document.write( "x + y =  = 25000.\r\n" );
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document.write( "Thus we found that the sum of seats in sections B and C is 25000,  \r\n" );
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document.write( "and, therefore, the number of seats in section A is 25000.\r\n" );
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document.write( "Thus we have now the problem  FOR TWO UNKNOWNS only, since we just excluded A.\r\n" );
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document.write( "Now our system of two equations is\r\n" );
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document.write( "  x +   y = 25000,                  (1)\r\n" );
document.write( "20x + 15y = 1074500 - 25*25000.     (2)\r\n" );
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document.write( "Equation (2) express the money payed for seats in sections B and C together.\r\n" );
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document.write( "Simplify (1),(2) step by step:\r\n" );
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document.write( "  x +   y = 25000,                  (3)\r\n" );
document.write( "20x + 15y = 449500.                 (4)\r\n" );
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document.write( "Multiply eq(1) by 20 (both sides). Then subtract eq(2) from it:\r\n" );
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document.write( "20x + 20y = 500000,                 (3)\r\n" );
document.write( "20x + 15y = 449500.                 (4)\r\n" );
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document.write( "====> 5y = 500000-449500 = 50500  ====>  y =  = 10100.\r\n" );
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document.write( "Then  x = 25000 - y = 25000 - 10100 = 14900.\r\n" );
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document.write( "Answer.  There are 25000 sears in section A,  14900 in section B  and  10100 in section C.\r\n" );
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