Question

A theater can seat a total of 630 people. Tickets cost $3 for children, $6 for students, and $8 for adults. At a recent sold-out screening, the combined total of children and students was equal to twice the number of adults. The money made from ticket sales totaled $3468. How many tickets of each type were sold?

Answer 1

Let's designate variables for ticket sales: x for children, y for students, and z for adults. The combined number of children and students equals twice the number of adults (x + y = 2z). With a total of 630 tickets sold (x + y + z = 630) and $3468 revenue (3x + 6y + 8z = 3468), we can solve this system of equations.

Step-by-step explanation:

Let's start by assigning variables to the number of tickets sold for each category.

Let's say the number of children's tickets sold is represented by x, the number of student tickets sold is represented by y, and the number of adult tickets sold is represented by z.

According to the given information, the combined total of children and students is equal to twice the number of adults.

So, we can write the equation:
x + y = 2z

We are also given that the total number of tickets sold is 630, so we can write the equation:
x + y + z = 630

Lastly, the total money made from ticket sales is $3468. Using the ticket prices, we can write the equation:
3x + 6y + 8z = 3468

To find the values of x, y, and z, we can solve this system of equations using substitution or elimination.