Question

One evening 1600 concert tickets were sold for the Fairmont Summer Jazz Festival. Tickets cost $25 for covered pavilion seats and $20 for lawn seats. Total recipts $36,000. How many tickets of each type were sold?How many pavilion seats were? sold?How many lawn seats were? sold?

Answer 1

• 800 pavilion seats

• 800 lawn seats

Explanation:

Let p represent the number of pavilion seats sold. Then 1600-p is the number of lawn seats sold. Total revenue is ...

25p +20(1600 -p) = 36000

5p + 32000 = 36000

5p = 4000

p = 800 . . . . . . . . . . number of pavilion seats sold

1600-p = 800 . . . . . number of lawn seats sold

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You can work these problems in your head. Consider that all seats were sold at the lower price. Then revenue would be 1600·20 = 32000. It was 36000 -32000 = 4000 more than that. The difference in ticket price is 25 -20 = 5 dollars, so there must have been 4000/5 = 800 higher-priced tickets sold. (Compare this working to the math above. You will find it substantially similar.)