A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each pri

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A 6000 seat theater has tickets for sale at $24 and $40. How many tickets should be sold at each price for a sellout performance to generate a total revenue of $188,800?

Let x be the number of $24 tickets, and y be the number of $40 tickets. We have:

  • 24x + 40y = 188,800
  • x + y = 6,000
  • Rearrange (2) to solve for x: x = 6000 - y
  • Plug in (3) to (1):
    • 24(6000 - y) + 40y = 188800
    144,000 - 24y + 40y = 188,800
    16y + 144,000 = 188,800

    Subtract 144,000 from each side:
    16y = 44,800

    Divide each side by 16
    y = 2,800 ($40 tickets)

    Plug this into (2)
    x + 2,800 = 6000

    Subtract 2,800 from each side:
    x = 3,200 ($24 tickets)

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