Question

A theatre contains 456 seats and the ticket prices for a recent play were $44 for adults and $30 for children. If the total proceeds were $16,466 for a sold-out matinee, how many of each type of tic were sold?

Answer 1

To solve this problem, use a system of equations to find the number of adult and children tickets sold. The equation x + y = 456 represents the total number of tickets sold, and the equation 44x + 30y = 16,466 represents the total proceeds from the ticket sales. Solving this system of equations, we find that 56 adult tickets and 400 children tickets were sold. Therefore, 56 adult tickets and 400 children tickets were sold.

Step-by-step explanation:

To solve this problem, we can use a system of equations.

Let's assume the number of adult tickets sold is x and the number of children tickets sold is y.

We know that the total number of tickets sold is 456, so we can write the equation:

x + y = 456

We also know that the total proceeds from the ticket sales is $16,466, so we can write the equation:

44x + 30y = 16,466

We now have a system of equations that we can solve to find the values of x and y.

Multiplying the first equation by 30 and subtracting it from the second equation, we get:

44x + 30y - 30x - 30y = 16,466 - 30(456)

14x = 16,466 - 13,680

14x = 786

x = 786/14

x = 56

Substituting the value of x back into the first equation, we can find the value of y:

56 + y = 456

y = 456 - 56

y = 400

Therefore, 56 adult tickets and 400 children tickets were sold.