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Adult tickets for a play cost $16 and child tickets cost $6. If there were 25 people at a performance and the theater collected $260 from ticket sales, how many adults and how many children attended the play?

  • algebra -

    By system of equations:
    C=number of child tickets sold
    A=number of adult tickets sold
    C+A = 25
    6C+16A = 260
    Solve for A and C (by substitution).

    Solving the problem in the head without pencils or paper or calculator:
    Adult tickets cost $10 more than child tickets. If all 25 were child tickets, they would have gathered 6*25=$150.
    To get $260, there must have been (260-150)/10=11 adults.
    So there were 11 adults and 14 children.

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