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=?
Mathematics · High School · Thu Feb 04 2021
Answered on
let the number of adults be a
and, number of students be x
and, number of children be c
Then, according to question,
a + c + x = 275 ….(1)
c = 2a { number of adults is half of children }
5c + 7x + 12a = 1986 …..(2)
putting value of c in equation (1), we get
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 by putting values of x and c in equation (2)
5(2a) + 7(275-3a) + 12a = 1986
10a + 1925 -21a + 12a = 1986
a = 1986 - 1925
a = 61
Now, value of c and x are:
c = 2a = 2 x 61 = 122
x = 275-3a
x = 275 - 3*61
x = 275 - 183
x = 92
Thus, 61 adults, 92 students and 122 children attended.