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25 May, 22:25

A 6000-seat theater has tickets for sale at $28 and $40. How many tickets should be sold at each price for a sellout show to generate a total revenue 194400

The number of tickets for sale at $28 should be

The number of tickets for sale at $40 should be

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  1. 25 May, 22:29
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    3,833 for $28

    2167 for $40

    Step-by-step explanation:

    Let X be the number of tickets sold at the price of $24, And Y be the number of tickets sold at the price of $40.

    Now, $ 28X will be the revenue generated due to the $28 tickets

    And, $40Y will be the revenue generated due to the 40$ tickets.

    Now, Total revenue generated should be $194400.

    Thus, 28X + 40Y = 194400 - (1).

    Also,

    Total number of seats in theater is 6000.

    So, X + Y = 6000. - (2)

    X = 6000 - Y.

    Put in equation 1

    We get, 168,000 - 28Y + 40Y = 194,400

    12Y = 26,000

    Y = 2,166.66

    Since, Y is of 40 $ so minimum tickets sold should be 2167.

    X = 3,833.
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