Question

A movie theater has a seating capacity of 197. The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. There are half as many adults as there are children. If the total ticket sales was $ 1416, How many children, students, and adults attended?
____ children attended
____students attended
____adults attended

Answer 1

Answer: 74 children attended

86 students attended

37 adults attended

Step-by-step explanation:

Let x represent the number of children that attended.

Let y represent the number of students that attended.

Let z represent the number of adults that attended.

The movie theater has a seating capacity of 197. It means that

x + y + z = 197- - - - - - - - - - - - -1

The theater charges $5.00 for children, $7.00 for students, and $12.00 of adults. If the total ticket sales was $ 1416, It means that

5x + 7y + 12z = 1416- - - - - - - - - - 2

There are half as many adults as there are children. It means that

It means that

z = x/2

x = 2z

Substituting x = 2z into equation 1 and equation 2, it becomes

2z + y + z = 197

y + 3z = 197- - - - - - - - - - - - -3

5 × 2z + 7y + 12z = 1416

10z + 7y + 12z = 1416

7y + 22z = 1416- - - - - - - - - - - 4

Multiplying equation 3 by 7 and equation 4 by 1, it becomes

7y + 21z = 1379

7y + 22z = 1416

Subtracting, it becomes

- z = - 37

z = 37

x = 2z = 2 × 37

x = 74

Substituting x = 74 and z = 37 into equation 1, it becomes

74 + y + 37 = 197

y = 197 - 74 - 37

y = 86