Question

A movie theater has a seating capacity of 167. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales was $ 1198, How many children, students, and adults attended?

Child attend:
Student attend:
Adult attend:

Answer 1

Child attend: 58

Studen attend: 80

Adult attend: 29

Explanation:

a + c + s = 167 Eq. 1

12a + 5c + 7s = 1198 Eq. 2

a = c/2 Eq. 3

a = adult attend

c = children attend

s = students attend

Replacing Eq, 3 in Eq. 2:

12(c/2) + 5c + 7s = 1198

6c + 5c + 7s = 1198

11c + 7s = 1198

7s = 1198 - 11c

s = (1198 - 11c) / 7 Eq, 4

Replacing Eq, 3 and Eq, 4 in Eq, 1

c/2 + c + (1198-11c) / 7 = 167

7c/14 + 14c/14 + 2(1198-11c)/14 = 2338/14

7c/14 + 14c/14 + 2396/14 - 22c/14 = 2338/14

7c + 14c + 2396 - 22c = 2338

7c + 14c - 22c = 2338 - 2396

-1c = -58

c = -58/-1

c = 58

from Eq. 3

a = c/2

a = 58/2

a = 29

from Eq. 4

s = (1198-11c)/7

s = (1198 - 11*58)/7

s = (1198 - 638) / 7

s = 560/7

s = 80

Check:

from Eq, 1

58 + 29 + 80 = 167