document.write( "Question 623771: I understand the concept but cannot arrive at the correct answers I think I am messing up the last equation. I keep getting the number of adult tickets is 74 but I know that is not right. A movie theater charges $7 for adults, $5 for children, and $4 for seniors over age 60. The theater sold 222 tickets and took in $1383. If twice as many adult tickets were sold as the total of children and senior tickets, how many tickets of each kind were sold. \n" ); document.write( "
Algebra.Com's Answer #392331 by math-vortex(648)\"\" \"About 
You can put this solution on YOUR website!
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document.write( "Hi, there-- \r\n" );
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document.write( "A movie theater charges $7 for adults, $5 for children, and $4 for seniors over age 60. The \r\n" );
document.write( "theater sold 222 tickets and took in $1383. If twice as many adult tickets were sold as the total \r\n" );
document.write( "of children and senior tickets, how many tickets of each kind were sold.\r\n" );
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document.write( "Let x be the number of adult tickets\r\n" );
document.write( "Let y be the number of child tickets\r\n" );
document.write( "let z be the number of senior tickets\r\n" );
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document.write( "Equations:\r\n" );
document.write( "The theater sold 222 tickets\r\n" );
document.write( "x + y + z = 222\r\n" );
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document.write( "The theater took in 1383. 7x is the income from adult tickets, 5y is the income from child tickets, \r\n" );
document.write( "and 4z is the income from senior tickets.\r\n" );
document.write( "7x + 5y + 4z = 1383\r\n" );
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document.write( "Twice as many adult tickets were sold as the total of child and senior tickets.\r\n" );
document.write( "[number of adult tickets] = [2] * [total of child tickets and senior tickets]\r\n" );
document.write( "x = 2(y + z)\r\n" );
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document.write( "These are the three equations.\r\n" );
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document.write( "I solved the system and got:\r\n" );
document.write( "x = 148 adult tickets\r\n" );
document.write( "y = 51 child tickets\r\n" );
document.write( "z = 23 senior tickets\r\n" );
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document.write( "Since you got 74 for the number of adult tickets, I'm thinking that you wrote your third equation as\r\n" );
document.write( "2x = y + z. It's easy to mix up where to put the multiplier. I always ask myself which value is \r\n" );
document.write( "larger (e.g. adult tickets or child plus senior tickets) The wording of the problem indicates that \r\n" );
document.write( "the number of adult tickets is larger, so we need to multiply the child plus senior side of the \r\n" );
document.write( "equation by 2 to achieve equality.\r\n" );
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document.write( "Let me know if you want to see the system of equations solved out. I got the impression you\r\n" );
document.write( "understood that part.\r\n" );
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document.write( "Ms.Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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