A movie theater has a seating capacity of 179. 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 $ 1284, How many children, students, and adults attended?

31 adults, 62 children, and 86 students.

Step-by-step explanation:

The seating capacity of the movie theatre = 179

Children's(c) Ticket = $5.00

Student's(s) Tickets = $7.00

Adult's(a) Tickets = $12.00

There are half as many adults as there are children.

The total ticket sales was $1284

We then solve the three resulting equations simultaneously.

c+s+a=179

c=2a

5c+7s+12a=1284

We substitute c=2a into the first and third equation

Substitute s=179-3a into 22a+7s=1284

Recall:

c=2a

c=2*31

c=62

Finally:

c+s+a=179

62+s+31=179

s=179-62-31

s=86.

Therefore:

31 adults, 62 children, and 86 students attended the movie theatre.

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