A movie theater has a seating capacity of 305. 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 $ 2220, How many children, students, and adults attended? children attended. students attended. adults attended.
A movie theater has a seating capacity of 305. 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 $ 2220, How many children, students, and adults attended? children attended. students attended. adults attended.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:### Movie Theater Attendance Problem
A movie theater has a seating capacity of 305. The theater charges $5.00 for children, $7.00 for students, and $12.00 for adults. There are half as many adults as there are children. If the total ticket sales were $2,220, how many children, students, and adults attended?
#### Table for Input:
| Children Attended | |
|-----------------------------|--|
| Students Attended | |
| Adults Attended | |
This scenario involves a mathematical word problem that can be solved using algebra. It provides an opportunity to practice setting up equations based on given conditions and solving them to find unknown values.
To solve this problem, we can define the variables as follows:
- Let \( C \) represent the number of children.
- Let \( S \) represent the number of students.
- Let \( A \) represent the number of adults.
#### Given Conditions:
1. There are half as many adults as children: \( A = \frac{C}{2} \).
2. Total number of attendees is 305: \( C + S + A = 305 \).
3. Total ticket sales amount to $2,220: \( 5C + 7S + 12A = 2,220 \).
By substituting \( A \) with \( \frac{C}{2} \) into the second and third equations, we can solve for the exact numbers of children, students, and adults that attended.
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