Question

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?

Answer 1

Answer:

31 adults, 62 children, and 86 students.

Step-by-step explanation:

The seating capacity of the movie theatre = 179

• c+s+a=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.

• $a=c/2 \implies c=2a$

The total ticket sales was $1284

• 5c+7s+12a=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

$2a+s+a=179 \implies s=179-3a\\5(2a)+7s+12a=1284 \implies 22a+7s=1284$

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

$22a+7(179-3a)=1284\\22a+1253-21a=1284\\a=1284-1253\\a=31$

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.

Answer 2

Adult 31
Children 62
Student 86