document.write( "Question 1054973: The admission to a barrio entertainment was $0.50 for adults and $0.25 for children. The total receipts for 150 tickets amounted $62.50. Find the number of adults and children admitted. \n" ); document.write( "

Algebra.Com's Answer #670186 by ikleyn(52786) $\"\"$ $\"About$

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\n" ); document.write( "The admission to a barrio entertainment was $0.50 for adults and $0.25 for children. The total receipts for 150 tickets amounted $62.50.
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\n" ); document.write( "\n" ); document.write( "Solution 1. System of two equations\r
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document.write( "    a +     c = 150,     (1)\r\n" );
document.write( "0.50a + 0.25c = 62.50.   (2)\r\n" );
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document.write( "You can simplify it:\r\n" );
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document.write( "  a +   c = 150,         (1')\r\n" );
document.write( "50a + 25c = 6250.        (2')\r\n" );
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document.write( "Express  c = 150 - a  from (1) and substitute into (2). You will get\r\n" );
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document.write( "50a + 25(150-a) = 6250   (3)   (one equation for one unknown \"a\").\r\n" );
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document.write( "The rest is just arithmetic.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 2. One equation\r
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document.write( "Let \"a\" be the number of adults.\r\n" );
document.write( "Then the number of child admissions is 150-a.\r\n" );
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document.write( "The \"value equation\" is \r\n" );
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document.write( "50a + 25*(150-a) = 6250   (exactly as the equation (3) in the Solution 1 above.\r\n" );
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document.write( "The rest is just arithmetic.\r\n" );
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