52-4 OC. There is no solution. 7-7z There are (Type whole numbers.) z), where 2 is any 3. A theater charges $10 for main-floor seats and $4 for balcony seats. If all seats are sold, the ticket income is $4000. At one show, 40% of the main-floor seats and 50% of the balcony seats were sold and ticket income was $1800. How many seats are on the main floor and how many are in the balcony? 10x+4y=4000 1800 • 4x + 5y= seats on the main-floor and seats in the balcony. 200 500
52-4 OC. There is no solution. 7-7z There are (Type whole numbers.) z), where 2 is any 3. A theater charges $10 for main-floor seats and $4 for balcony seats. If all seats are sold, the ticket income is $4000. At one show, 40% of the main-floor seats and 50% of the balcony seats were sold and ticket income was $1800. How many seats are on the main floor and how many are in the balcony? 10x+4y=4000 1800 • 4x + 5y= seats on the main-floor and seats in the balcony. 200 500
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![**Educational Website Content**
### Solving Systems of Equations Using the Gauss-Jordan Method
#### Example Problem:
5. Solve the following system using the Gauss-Jordan method:
\[
\begin{align*}
5x + 5y - 5z &= 40 \\
2x - y + 5z &= 6 \\
-x - 4y + 3z &= -38 \\
\end{align*}
\]
**Select the correct choice from the options below:**
- **A.** There is one solution.
- The solution is \((x, y, z) = (1, 10, 1)\)
- (Type in exact numbers in simplified form)
- **B.** There are infinitely many solutions.
- The solutions are \((x, y, z)\) where \(z\) is any real number.
- **C.** There is no solution.
#### Word Problem Example:
**3. Theater Seating Problem:**
A theater charges $10 for main-floor seats and $5 for balcony seats. If all seats are sold, the ticket income is $4000. At one show, 40% of the main-floor seats and 50% of the balcony seats were sold and ticket income was $1800. How many seats are on the main floor and how many are in the balcony?
**Solution:**
- Use the equations:
\[
\begin{align*}
10x + 5y &= 4000 \quad \text{(all seats sold)} \\
4x + 2.5y &= 1800 \quad \text{(partial seats sold)}
\end{align*}
\]
- Solving these, you find:
- **Seats on the main floor:** 200
- **Seats in the balcony:** 400
**Transcribed Calculations:**
- Gaussian elimination steps are shown leading to the solution \((x, y, z) = (1, 7, 2)\) for a different set of equations.
---
This example illustrates how algebraic methods can solve real-world problems efficiently.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F43bd6ecf-0a0f-4666-aaae-944e31ddf02f%2F352b5509-8491-4675-a83f-2cfcbf86b355%2Fel0vacm_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Educational Website Content**
### Solving Systems of Equations Using the Gauss-Jordan Method
#### Example Problem:
5. Solve the following system using the Gauss-Jordan method:
\[
\begin{align*}
5x + 5y - 5z &= 40 \\
2x - y + 5z &= 6 \\
-x - 4y + 3z &= -38 \\
\end{align*}
\]
**Select the correct choice from the options below:**
- **A.** There is one solution.
- The solution is \((x, y, z) = (1, 10, 1)\)
- (Type in exact numbers in simplified form)
- **B.** There are infinitely many solutions.
- The solutions are \((x, y, z)\) where \(z\) is any real number.
- **C.** There is no solution.
#### Word Problem Example:
**3. Theater Seating Problem:**
A theater charges $10 for main-floor seats and $5 for balcony seats. If all seats are sold, the ticket income is $4000. At one show, 40% of the main-floor seats and 50% of the balcony seats were sold and ticket income was $1800. How many seats are on the main floor and how many are in the balcony?
**Solution:**
- Use the equations:
\[
\begin{align*}
10x + 5y &= 4000 \quad \text{(all seats sold)} \\
4x + 2.5y &= 1800 \quad \text{(partial seats sold)}
\end{align*}
\]
- Solving these, you find:
- **Seats on the main floor:** 200
- **Seats in the balcony:** 400
**Transcribed Calculations:**
- Gaussian elimination steps are shown leading to the solution \((x, y, z) = (1, 7, 2)\) for a different set of equations.
---
This example illustrates how algebraic methods can solve real-world problems efficiently.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
