Question

A theater charges $8 for an adult ticket, and $6 for a children’s ticket. on a certain day, a total of 255 tickets were sold for a total cost of $1,850. how many more children’s tickets were sold than adult tickets?

Answers

  2. The number of adult tickets sold more than the children’s tickets are 65.
    It is given in the question that the charge of an adult ticket and a children’s ticket is $8 and $6 respectively.
    It is also given that, on a certain day the number of tickets sold are 255 at a total cost of $1,850.
    We have to find the number by which children’s ticket were sold more than adult tickets.
    Let the number of children tickets sold on that particular day be x.
    Let the number of adult tickets sold on that particular day be y.
    Hence, according to the question,
    x + y = 255  …(1)
    Also,
    6*x + 8*y = 1850
    Dividing 2 from both sides, we get
    3x + 4y = 925  …(2)
    Multiplying (1) by 3, we get
    3x + 3y = 765  …(3)
    (2) – (3)
    (3x – 3x) + (4y – 3y) = 925 – 765
    0 + y = 160
    y = 160
    Hence, the number of adult tickets sold are 160.
    We know that,
    x + y = 255
    Hence,
    x + 160 = 255
    x = 255 – 160
    x = 95
    Hence, the number of children’s tickets sold are 95.
    The number of adult tickets sold more than the children’s ticket are =
    160 – 95 = 65 tickets.
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