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26 September, 08:06

last tuesday, Regal Cinemas sold a total of 8000 movie tickets. proceeds totaled $57,000. tickets can be bought in one of 3 ways: a matinee admission costs $5, student admission is $6 all day, and regular admissions are $8. how many of each type of ticket was sold if twice as many student tickets were sold as matinee tickets?

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  1. 26 September, 11:14
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    The answer is that there were 1000 matinee tickets, 2000 student tickets, and 5000 regular tickets sold.

    Step-by-step explanation:

    Let m = number of Matinee tickets, s = number of student tickets, and r = number of regular tickets. The sum of these variables is equal to 8000:

    m + s + r = 8000

    Solve for r:

    r = 8000 - m - s

    There were twice the number of student tickets as matinee:

    s = 2m

    Substitute:

    m + s + r = 8000

    m + 2m + r = 8000

    3m + r = 8000

    r = 8000 - 3m

    The number of each type of ticket sold at that price is equal to the total dollar amount:

    5m + 6s + 8r = 57000

    Substitute:

    5m + 6 (2m) + 8 (8000 - 3m) = 57000

    5m + 12m + 64000 - 24m = 57000

    17m - 24m = - 7000

    -7m = - 7000

    m = 1000 Matinee tickets sold

    s = 2m = 2 (1000) = 2000 Student tickets sold

    r = 8000 - 3m = 8000 - 3 (1000) = 8000 - 3000 = 5000 Regular tickets sold.

    Proof total number of tickets:

    m + s + r = 8000

    1000 + 2000 + 5000 = 8000

    8000 = 8000

    Proof dollar amount:

    5m + 6s + 8r = 57000

    5 (1000) + 6 (2000) + 8 (5000) = 57000

    5000 + 12000 + 40000 = 57000

    17000 + 40000 = 57000

    57000 = 57000
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