An amphitheater charges $75 for each seat in Section A, $55 for each seat in Section B, and $30 for each lawn seat. There are 1500 seats in Section A, 4500 seats in Section B, and 17,000 lawn seats. On the first day, 10,000 tickets sold, generating $356,000 in revenue. The number of seats sold in Sections A and B are the same. How many lawn seats are still available?

Given 10,000 tickets sold at prices of $75 and $55 for sections A and B and $30 for lawn seats, raising $356,000 in revenue, we want the number of unsold lawn seats if 17,000 are available. As many $75 tickets as $55 tickets were sold.

Setup

Let x represent the number of lawn seats sold. Then the number of tickets sold in section A is (10,000 -x)/2, with an equal number sold in section B. Then the total revenue is ...

75(10000-x)/2 +55(10000-x)/2 +30x = 356000

Solution

Simplifying the equation, we get ...

-35x +650000 = 356000

-35x = -294000 . . . . . . . . . . . subtract 650000

x = 8400 . . . . . . . . . . . . divide by -35

The number of lawn seats still available is ...

17000-8400 = 8600

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Additional comment

The number of tickets sold for section A is (10000-8400)/2 = 800, with an equal number sold in section B. That leaves 46.7% of section A seats empty, and 82.2% of section B seats empty. 50.6% of lawn seats were empty, leaving an overall impression of poor attendance. Overall revenue was about 40.9% of that from a sold-out production.