Question

A movie theater has a seating capacity of 275. 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 $ 1986, How many children, students, and adults attended? CHILDREN ATTENDED= ? STUDENTS ATTENDED= ? ADULTS ATTENDED=?

Answer 1

Adults = 61

Students = 92

Children = 122

Explanation:

a adults

x students

c children

a + c + x = 275

c / a = 2

5c + 7x + 12a = 1986

Simplify and solve the system.

a + 2a + x = 275

3a +x = 275

x = 275 - 3a. and c= 2a

The revenue equation can be written in terms of just one variable, a.

5(2a) + 7(275-3a) + 12a = 1986

Solve for a

a = 61

use it to find x and c.

c = 2a = 2 x 61 = 122

x = 275-a-c

x = 275 - 61-122

x = 92