A movie theater has a seating capacity of 385. 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 $ 2794, How many children, students, and adults attended?

Answer:

Step-by-step explanation:

The number of children is 198, adults are 99 and students are 88.

A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.

Given that, the theatre sitting capacity is 385 and the theatre charges are $5.00 for children $7.00 for students, and $12.00 for adults.

Let the number of children be c, since, there are half as many adults as there are children therefore, number of adults = c/2

The number of students = 385 - c - c/2 = 385 - 3c/2

The total cost  = $2794

Therefore,

2794 = 5c+c/2×12+(385-3c/2)×7

2794 = 5c+6c+2695 - 21c/2

c = 198

Therefore, number of adults = 198/2 = 99

The number of students = 385-3/2×198 = 88

Hence, The number of children is 198, adults are 99 and students are 88.

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For most exercises, this key does not include even-numbered items.
■ Exercise 1 Read the passage. Based on what you already know, underline the verbs.
The Marshmallow Experiment
Imagine that you are seven years old. You are participating in an experiment. A researcher greets you and shows you into a small room. In the room there is a marshmallow. The marshmallow is for you, but here is the interesting part: The researcher tells you that he is going to leave you alone in the room for a while. You can eat the marshmallow right away, or you can wait until he gets back. If you wait until he gets back, you will get a second marshmallow.
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