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A theatre contains 429 seats and the ticket prices for a recent play were $47 for adults and $20 for children. If the total proceeds were $12,900 for a sold-out matinee.

how many of each type of ticket were sold?

1 Answer

5 votes

Answer:

Therefore, 132 adult tickets and 297 child tickets were sold.

Explanation:

To find out how many of each type of ticket were sold, we can set up a system of equations based on the given information.

Let's assume the number of adult tickets sold is A, and the number of child tickets sold is C.

From the given information, we know that the total number of seats sold is the sum of adult and child tickets: A + C = 429 (equation 1).

We also know that the total proceeds from the ticket sales were $12,900. The cost of each adult ticket is $47, so the total revenue from adult tickets is 47A. Similarly, the cost of each child ticket is $20, so the total revenue from child tickets is 20C. Thus, the total revenue from ticket sales is 47A + 20C.

Using this information, we can set up another equation: 47A + 20C = 12,900 (equation 2).

Now we have a system of equations:

A + C = 429 (equation 1)

47A + 20C = 12,900 (equation 2)

To solve this system, we can use substitution or elimination.

Let's solve the system using substitution:

From equation 1, we can isolate A: A = 429 - C.

Substituting this value of A into equation 2, we get: 47(429 - C) + 20C = 12,900.

Expanding and simplifying the equation, we have: 20C + 20313 - 47C = 12,900.

Combining like terms, we get: -27C = -8023.

Dividing both sides of the equation by -27, we find: C = 297.

Now that we know the value of C, we can substitute it back into equation 1 to find the value of A: A = 429 - 297 = 132.

Therefore, 132 adult tickets and 297 child tickets were sold.

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