Question

A theatre contains 482 seats and the ticket prices for a recent play were 52$ for an adult and 20$ for children. If the total proceeds we’re 16,008 for a sold- out matinee, how many of each type of ticket were sold?

Answer 1

The total number of seats available is 482, and the ticket prices are $52 for adults and $20 for children. The total proceeds from the sold-out matinee are $16,008.

We can set up the following system of equations based on the given information:

Equation 1: A + C = 482 (total number of seats sold is equal to the total number of seats available)

Equation 2: 52A + 20C = 16,008 (total proceeds from ticket sales)

To solve this system of equations, we can use a method such as substitution or elimination.

Let's solve it using the substitution method:

From Equation 1, we can express A in terms of C:
A = 482 - C

Substituting this expression for A in Equation 2:
52(482 - C) + 20C = 16,008

Expanding and simplifying:
25,064 - 52C + 20C = 16,008

Combining like terms:
-32C = 16,008 - 25,064
-32C = -9,056

Dividing both sides by -32:
C = -9,056 / -32
C = 283

Substituting the value of C back into Equation 1:
A + 283 = 482
A = 482 - 283
A = 199

Therefore, there were 199 adult tickets and 283 children's tickets sold for the matinee.

Answer 2

Answer: There were 199 adult tickets and 283 children's tickets sold for the sold-out matinee

Step-by-step explanation:

Let's denote the number of adult tickets sold as "A" and the number of children's tickets sold as "C."

Given the information:

1. The theater contains 482 seats.

2. The ticket price for an adult is $52.

3. The ticket price for a child is $20.

4. The total proceeds were $16,008.

We can set up a system of equations to represent the given information:

Equation 1: A + C = 482 (Total number of seats)

Equation 2: 52A + 20C = 16,008 (Total proceeds from ticket sales)

Now, let's solve this system of equations to find the values of A and C.

From Equation 1, we can express A as: A = 482 - C

Substitute this value of A into Equation 2:

52(482 - C) + 20C = 16,008

Distribute 52:

25,064 - 52C + 20C = 16,008

Combine like terms:

-32C = -9,056

Divide by -32:

C = 283

Now that we know the number of children's tickets (C), we can substitute it back into the expression for A:

A = 482 - C

A = 482 - 283

A = 199

So, there were 199 adult tickets and 283 children's tickets sold for the sold-out matinee.

To verify:

Total adult ticket sales = 199 * $52 = $10,348

Total children's ticket sales = 283 * $20 = $5,660

Total proceeds = $10,348 + $5,660 = $16,008

The calculated values match the given total proceeds of $16,008, confirming the solution.