Use a system of linear equations with two variables and two equations to solve. 204 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed. Passing Students: Failing Students: Number Number
Use a system of linear equations with two variables and two equations to solve. 204 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed. Passing Students: Failing Students: Number Number
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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![### Solving Linear Systems with Two Variables
**Problem Statement:**
204 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.
**Solution Methods:**
Use a system of linear equations with two variables to solve the problem.
**Formulation:**
Let \( x \) be the number of students who passed the class.
Let \( y \) be the number of students who failed the class.
**Equations:**
1. Total number of students:
\[
x + y = 204
\]
2. Five times as many students passed as failed:
\[
x = 5y
\]
**Steps to Solve:**
1. Substitute \( x \) from the second equation into the first equation:
\[
5y + y = 204
\]
2. Combine like terms and solve for \( y \):
\[
6y = 204 \implies y = 34
\]
3. Substitute \( y \) back into the second equation to find \( x \):
\[
x = 5 \cdot 34 = 170
\]
**Result:**
- Number of Passing Students: \( 170 \)
- Number of Failing Students: \( 34 \)
**Input Fields:**
- **Passing Students:** [Input Field]
- **Failing Students:** [Input Field]
**Graphical Representation:**
There are no graphs or diagrams provided in the original text.
This example demonstrates how systems of linear equations can be applied to real-world problems, helping us to understand and analyze different scenarios mathematically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F54422bad-1dbc-44f7-b929-730cc42f6e53%2Fc8e642ab-b159-45ea-a284-d49b13ddcbbe%2Fh2742y_processed.png&w=3840&q=75)
Transcribed Image Text:### Solving Linear Systems with Two Variables
**Problem Statement:**
204 students enrolled in a freshman-level chemistry class. By the end of the semester, 5 times the number of students passed as failed. Find the number of students who passed, and the number of students who failed.
**Solution Methods:**
Use a system of linear equations with two variables to solve the problem.
**Formulation:**
Let \( x \) be the number of students who passed the class.
Let \( y \) be the number of students who failed the class.
**Equations:**
1. Total number of students:
\[
x + y = 204
\]
2. Five times as many students passed as failed:
\[
x = 5y
\]
**Steps to Solve:**
1. Substitute \( x \) from the second equation into the first equation:
\[
5y + y = 204
\]
2. Combine like terms and solve for \( y \):
\[
6y = 204 \implies y = 34
\]
3. Substitute \( y \) back into the second equation to find \( x \):
\[
x = 5 \cdot 34 = 170
\]
**Result:**
- Number of Passing Students: \( 170 \)
- Number of Failing Students: \( 34 \)
**Input Fields:**
- **Passing Students:** [Input Field]
- **Failing Students:** [Input Field]
**Graphical Representation:**
There are no graphs or diagrams provided in the original text.
This example demonstrates how systems of linear equations can be applied to real-world problems, helping us to understand and analyze different scenarios mathematically.
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