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Math Help - Movie Theater

  1. #1
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    Movie Theater

    At a movie theater, a cashier sold 250 more adult admission tickets than children'admission tickets. The adult's tickets were $6.00 each and the children's tickets were $3.50 each. What is the least number of each type of ticket that the cashier had to sell for the total
    receipts to be at least $2,750?
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  2. #2
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    Hmmm. It took quite some time to solve this problem but finally i managed to figure it out. Hopefully it is correct

    let x be the number of adult ticket sold
    let y be the number of children ticket sold

    6x + 3.5y = $2750 ............ Eqn 1
    x - y = 250 ...................... Eqn2

    We cannot solve the Eqn 1 and Eqn 2 directly as Eqn 1 involve cost and Eqn 2 involve quantity but it will help us solve the equation listed below

    6(x-250) + 3.5y = 2750 - 6(250) where 250 are the number of tickets

    Since x-250 = y ( derive from Eqn 2 )

    6y + 3.5y = 1250
    9.5y = 1250
    y = 132
    Resubstitute y = 132 into Eqn 1 or Eqn2 to get x, which is 382

    I hope it helps
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  3. #3
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    yes but....

    Quote Originally Posted by tester85 View Post
    Hmmm. It took quite some time to solve this problem but finally i managed to figure it out. Hopefully it is correct

    let x be the number of adult ticket sold
    let y be the number of children ticket sold

    6x + 3.5y = $2750 ............ Eqn 1
    x - y = 250 ...................... Eqn2

    We cannot solve the Eqn 1 and Eqn 2 directly as Eqn 1 involve cost and Eqn 2 involve quantity but it will help us solve the equation listed below

    6(x-250) + 3.5y = 2750 - 6(250) where 250 are the number of tickets

    Since x-250 = y ( derive from Eqn 2 )

    6y + 3.5y = 1250
    9.5y = 1250
    y = 132
    Resubstitute y = 132 into Eqn 1 or Eqn2 to get x, which is 382

    I hope it helps
    Tell me, why is equation 2 x - y = 250 and NOT
    x + y = 250?
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  4. #4
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    It is due to this statement " a cashier sold 250 more adult admission tickets than children'admission tickets "

    Since we let x be the number of adult ticket sold
    we let y be the number of children ticket sold

    x - y = 250
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