document.write( "Question 1044739: Tickets are sold at $4.00 for adults and $2.50 for students. If 100 tickets were sold for $355.00, how many tickets were adult tickets? I need to define the variable, state the system and answer the question. \n" ); document.write( "

Algebra.Com's Answer #660100 by ikleyn(52787) $\"\"$ $\"About$

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\n" ); document.write( "Tickets are sold at $4.00 for adults and $2.50 for students. If 100 tickets were sold for $355.00,
\n" ); document.write( "how many tickets were adult tickets? I need to define the variable, state the system and answer the question.
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document.write( "Variables: let \"x\" be the numbers of adult tickets, and\r\n" );
document.write( "           let \"y\" be the numbers of student tickets.\r\n" );
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document.write( "The system is:\r\n" );
document.write( " x +    y = 100,       (1)   (\"100 tickets were sold\") and\r\n" );
document.write( "4x + 2.5y = 355.       (2)   (\"100 tickets were sold for $355.00\")\r\n" );
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document.write( "To solve the system, express \"x\" from (1): x = 100 - y, and substitute it into (2). You will get a single equation for y:\r\n" );
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document.write( "4*(100 - y) + 2.5y = 355.\r\n" );
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document.write( "Simplify and solve it:\r\n" );
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document.write( "400 - 4y + 2.5y = 355,   or\r\n" );
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document.write( "-1.5y = 355 - 400,\r\n" );
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document.write( "-1.5y = -45,\r\n" );
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document.write( "y =  = 30.\r\n" );
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document.write( "So, we just found y, the number of student tickets.\r\n" );
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document.write( "Then  x = 100 - y = 100 - 30 = 70. It is the number of adult tickets.\r\n" );
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document.write( "Check: 70*4 + 30*2.5 = 280 + 75 = 355.  Correct !\r\n" );
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document.write( "Answer.  70 adult and 30 student tickets were sold.\r\n" );
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