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March 24, 2017

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A 3500-seat theater sells tickets for $75 and $110. Each night the theater's expenses total $245,000. When all 3500 seats sell, the owners want ticket revenues to cover expenses plus earn a profit of 25% of expenses. How many tickets of each price should be sold to achieve this?

  • Math - ,

    X Tickets @ $75 each.
    (3500-X) Tickets @ $110 each.

    75x + 110(3500-x) = 245,000+0.25*245,000
    75x + 385,000-110x = 306,250
    -35x = 306,250-385,000 = -78,750
    X = 2250 Seats @ $75 each.
    3500-x=3500-2250 = 1250 seats @ @110each

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