Create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer's Rule. A movie theatre sold tickets to three movies. The price per ticket to the first, second, and third movies were $6, $11, and $13, respectively. 100 tickets were sold to the first movie. The total number of tickets sold was 661, for a total revenue of $7,393. How many tickets for each movie were sold? first movie tickets second movie tickets third movie tickets
Create a system of linear equations to describe the behavior. Then, solve the system for all solutions using Cramer's Rule. A movie theatre sold tickets to three movies. The price per ticket to the first, second, and third movies were $6, $11, and $13, respectively. 100 tickets were sold to the first movie. The total number of tickets sold was 661, for a total revenue of $7,393. How many tickets for each movie were sold? first movie tickets second movie tickets third movie tickets
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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![**Create a System of Linear Equations to Describe Behavior**
In this problem, we are tasked with determining how many tickets were sold for each of three movies at a movie theatre. We are given the following information:
- The ticket prices for the first, second, and third movies were $6, $11, and $13, respectively.
- A total of 661 tickets were sold.
- The total revenue from the ticket sales was $7,393.
- Specifically, 100 tickets were sold for the first movie.
**Your goal:**
1. Determine how many tickets were sold for each movie.
2. Use Cramer's Rule to solve for all solutions.
**Equations to consider:**
1. Let \( x \), \( y \), and \( z \) represent the number of tickets sold for the first, second, and third movie, respectively.
2. Equation for total tickets:
\[
x + y + z = 661
\]
3. Equation for total revenue:
\[
6x + 11y + 13z = 7,393
\]
4. Given condition:
\[
x = 100
\]
**Additional Materials**
- eBook
- Further guidance on solving systems of equations using Cramer's Rule
To solve this system of equations by Cramer's Rule, substitute the given condition into the other equations and solve for \( y \) and \( z \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F851d2752-072d-460a-a1d8-2cb438e193a7%2F16bf58f5-12e7-4cf4-9873-6c1a6145edd2%2Fkr5ery_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Create a System of Linear Equations to Describe Behavior**
In this problem, we are tasked with determining how many tickets were sold for each of three movies at a movie theatre. We are given the following information:
- The ticket prices for the first, second, and third movies were $6, $11, and $13, respectively.
- A total of 661 tickets were sold.
- The total revenue from the ticket sales was $7,393.
- Specifically, 100 tickets were sold for the first movie.
**Your goal:**
1. Determine how many tickets were sold for each movie.
2. Use Cramer's Rule to solve for all solutions.
**Equations to consider:**
1. Let \( x \), \( y \), and \( z \) represent the number of tickets sold for the first, second, and third movie, respectively.
2. Equation for total tickets:
\[
x + y + z = 661
\]
3. Equation for total revenue:
\[
6x + 11y + 13z = 7,393
\]
4. Given condition:
\[
x = 100
\]
**Additional Materials**
- eBook
- Further guidance on solving systems of equations using Cramer's Rule
To solve this system of equations by Cramer's Rule, substitute the given condition into the other equations and solve for \( y \) and \( z \).
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