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# How do you do this problem about theatre seating?

A theatre contains 500 seats and the ticket prices for a recent play were $43 for adults and $28 for children. If the total proceeds for one matinee were $16,805, how many of each ticket were sold?

is it like 500 = 43x + 28(43-x) or something??

### 3 Answers

- Bail OutLv 69 years agoFavorite Answer
43x + 28(500-x) = 16805

43x + 14000 - 28x = 16805

15x = 2805

x = 2805/15 = 187adults.

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- 9 years ago
Not quite.

16,805 = total proceeds

16,805 = 43x + 28y

...I think.

I stand corrected, guy above me is right; assuming that all seats sold:

16,805 = 43x + 28(500 - x) would be the correct answer.

this is because x is the number who of adults who bought a ticket so 500-x would be the children.

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- Mike GLv 79 years ago
A = Adult number

C = Child number

43A+28C = 16,805

If we assume the theatre was full A+C = 500

C = 500-A

43A+28(500-A) = 16,805

43A+14,000-28A=16,805

A = 187

C = 313

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