document.write( "Question 1101033: A stadium has 48,000 seats. Seats sell for $28 in section A, $16 section B, $12 section C. The numbers of seats in section A equals the total number of seats in section B and C. Suppose the stadium takes $1,016,800 from each sold-out event. How many seats does each section hold? \n" ); document.write( "

Algebra.Com's Answer #715605 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "A stadium has 48,000 seats. Seats sell for $28 in section A, $16 section B, $12 section C.
\n" ); document.write( "The numbers of seats in section A equals the total number of seats in section B and C. Suppose the stadium takes $1,016,800
\n" ); document.write( "from each sold-out event. How many seats does each section hold?
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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 = 48000,   or\r\n" );
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document.write( "(x+y)  + x      + y      = 48000,   which is the same as\r\n" );
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document.write( "2(x+y) = 48000,                     which implies\r\n" );
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document.write( "x + y =  = 24000.\r\n" );
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document.write( "Thus we found that the sum of seats in sections B and C is 24000,  \r\n" );
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document.write( "and, therefore, the number of seats in section A is 24000.\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 = 24000,                  (1)\r\n" );
document.write( "16x + 12y = 1016800 - 28*24000.     (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 = 24000,                  (3)\r\n" );
document.write( "16x + 12y = 344800.                 (4)\r\n" );
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document.write( "Multiply eq(1) by 16 (both sides). Then subtract eq(2) from it:\r\n" );
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document.write( "16x + 16y = 384000,                 (3)\r\n" );
document.write( "16x + 12y = 344800.                 (4)\r\n" );
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document.write( "====> 4y = 384000-344800 = 39200  ====>  y =  = 9800.\r\n" );
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document.write( "Then  x = 24000 - y = 24000 - 9800 = 14200.\r\n" );
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document.write( "Answer.  There are 24000 sears in section A,  14200 in section B  and  9800 in section C.\r\n" );
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