document.write( "Question 1097191: Stuck on a ticket question:
\n" ); document.write( "three kinds of tickets are sold for a school student parent dinner: a $1.00 ticket for one adult, a $1.50 ticket for one adult and one child and $2 ticket for 2 adults and one child. Total raised was $69 and 32 children and 62 adults attended. How many of each type of ticket was sold? \n" ); document.write( "

Algebra.Com's Answer #711605 by ikleyn(52847) $\"\"$ $\"About$

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document.write( "Let x be the number of $1.50 tickets for 1 adults and one child.\r\n" );
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document.write( "Let y be the number of $2    tickets for 2 adults and one child.\r\n" );
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document.write( "Then the number of $1 tickets for single adult is (62-x-2y).\r\n" );
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document.write( "Then you have these two equations:\r\n" );
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document.write( "   x +  y             = 32     (1)    (counting children)\r\n" );
document.write( "1.5x + 2y + (62-x-2y) = 69     (2)    (counting money)\r\n" );
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document.write( "Simplify: \r\n" );
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document.write( "   x +  y = 32,                (3)\r\n" );
document.write( "0.5x      = 69-62 = 7          (4)\r\n" );
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document.write( "Simplify again:\r\n" );
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document.write( "   x +  y = 32,                (5)\r\n" );
document.write( "0.5x      =  7.                (6)\r\n" );
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document.write( "It is clear now from (2) that  x = 2*7 = 14.\r\n" );
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document.write( "Then from (1)  y = 32 - x = 32 - 14 = 18.\r\n" );
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document.write( "Answer.  14 $1.50 tickets;  18 $2 tickets;  and the number of $1 tickets is 62-x-2y = 62-14-2*18 = 12.\r\n" );
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\n" ); document.write( "\n" ); document.write( "The lesson to learn from this solution:\r
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document.write( "     I wanted, most of all, to reduce the problem to 2 equations and avoid having 3 equations.\r\n" );
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document.write( "     And I succeeded in it.\r\n" );
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