An amateur theater group is converting a large classroom into an auditorium for a forthcoming play. The group will sell $3, $5, and $6

Question

An amateur theater group is converting a large classroom into an auditorium for a
forthcoming play. The group will sell $3, $5, and $6 tickets. They want to receive
exactly $503 from the sale of the tickets. If the number of $5 tickets to be sold is twice
the number of $6 tickets, and the number of $3 tickets is 1 more than 3 times the
number of $6 tickets, how many $3 tickets are there?

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Jezebel 1 week 2021-07-21T05:24:32+00:00 1 Answers 0 views 0

Answers ( )

    0
    2021-07-21T05:26:22+00:00

    x = the number of $3 tickets

    y = the number of $5 tickets

    z = the number of $6 tickets

    the group sells $3, $5, and $6 tickets, and receives exactly $503 from the sale of tickets

    3x + 5y + 6z = 503

    the number of $5 tickets is twice the number of $6 tickets

    y = 2z

    the number of $3 tickets is 1 more than 3 times the number of $6 tickets

    x = 1 + 3z

    by solving the system of equations

    3x + 5y + 6z = 503

    y = 2z

    x = 1 + 3z

    we find

    x = 61 tickets

    y = 40 tickets

    z = 20 tickets

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