Mathematics

Question

A group of 3 adults and 5 children pay a total of 52$ for movie tickets
A group of 2 adults and 4 children pay a total of 38$ for tickets what is the cost of one adult ticket and what is the cost for one child ticket

1 Answer

  • Answer:

    • $9 adult
    • $5 child

    Step-by-step explanation:

    Letting "a" and "c" represent the costs of adult tickets and child tickets, the problem statement gives us two relations:

      3a +5c = 52

      2a +4c = 38

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    We can solve this system of equations using "elimination" as follows:

    Dividing the first equation by 2 we get

      a +2c = 19

    Multiplying this by 3 and subtracting the first equation eliminates the "a" variable and tells us the price of a child ticket:

      3(a +2c) -(3a +4c) = 3(19) -(52)

      c = 5 . . . . . . collect terms

      a +2·5 = 19 . . substitute for c in the 3rd equation above

      a = 9 . . . . . . subtract 10

    One adult ticket costs $9; one child ticket costs $5.

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