Question

Details

A movie theater has a seating capacity of 205. 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 $ 1482, How many
children, students, and adults attended?

Answer 1

94 children, 64 students, and 47 adults attended the movie theater.

Explanation:

Let; a be for adults, s for students, and c for children.

Make a system to solve for the amount of people.

c/a = 2

a + 2a + s = 205

3a + s = 205

Simplify.

s = 205 - 3a

s = 205 - 3a

c = 2a

Plug it in.

5c + 7s + 12a = 1482

10a + 7(205 -3a) + 12a = 1482

10a + 1435 - 21a + 12a = 1482

a + 1435 = 1482

a = 47

Substitute.

c = 2(47)

c = 94

Solve.

s = 205 - 3(47)

s = 64