document.write( "Question 1050974: If 104 people attend a concert and tickets for adults cost $2.25 while tickets for children cost $1.75 and total receipts for the concert was $202.5, how many of each went to the concert?\r
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Algebra.Com's Answer #666573 by ikleyn(52797) $\"\"$ $\"About$

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\n" ); document.write( "If 104 people attend a concert and tickets for adults cost $2.25 while tickets for children cost $1.75
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\n" ); document.write( "\n" ); document.write( "Solution 1 (using one equation in one unknown)\r
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document.write( "Let x be the number of adult ticket bought.\r\n" );
document.write( "Then the number of children tickets bought is (104-x).\r\n" );
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document.write( "The \"value\" equation is\r\n" );
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document.write( "225*x + 175(104-x) = 20250.   (1)\r\n" );
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document.write( "Reduce by 25 all terms in both sides:\r\n" );
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document.write( "9x + 7*(104-x) = 810.\r\n" );
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document.write( "9x + 728 - 7x = 810,\r\n" );
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document.write( "2x = 810 - 728,\r\n" );
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document.write( "2x = 82   --->  x =  = 41.\r\n" );
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document.write( "Answer.  41 adult tickets and 104-41 = 63 children tickets.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solution 2 (using a system of two equations in two unknown)\r
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document.write( "Let \"x\" be the number of the adult    ticket bought, and\r\n" );
document.write( "let \"y\" be the number of the children ticket bought.\r\n" );
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document.write( "Then you have a system of two linear equations in two unknowns\r\n" );
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document.write( "   x +    y = 104,           (1)\r\n" );
document.write( "225x + 175y = 20250.         (2)  (this is the \"value\" equation in cents)\r\n" );
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document.write( "From the equation (1), express y = 104-x, and substitute this expression into the equation (2). You will get\r\n" );
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document.write( "225*x + 175(104-x) = 20250.  (3)\r\n" );
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document.write( "The equation (3) is a single equation for the unknown \"x\".\r\n" );
document.write( "It coincides with the equation (1) of the Solution 1 above.\r\n" );
document.write( "Use the same procedure as in the Solution 1 to find \"x\".\r\n" );
document.write( "Then find \"y\".\r\n" );
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document.write( "You will get the same answer, of course.\r\n" );
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