A cookie company uses one cup of sugar for every 20 cookies it makes. Let S represent the total number of cups of sugar used, and let N represent the number of cookies made. Write an equation relating S to N, and then equation using the axes below.
A cookie company uses one cup of sugar for every 20 cookies it makes. Let S represent the total number of cups of sugar used, and let N represent the number of cookies made. Write an equation relating S to N, and then equation using the axes below.
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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![# Writing an Equation and Drawing Its Graph to Model a Real-World Scenario
### Problem Statement:
A cookie company uses one cup of sugar for every 20 cookies it makes.
Let \( S \) represent the total number of cups of sugar used, and let \( N \) represent the number of cookies made. Write an equation relating \( S \) to \( N \), and then graph the equation using the axes below.
### Explanation of the Graph:
- **Axes Overview**: The graph is a coordinate grid with the horizontal axis labeled \( N \) (representing the number of cookies) ranging from 0 to 110, and the vertical axis labeled \( S \) (representing the cups of sugar) ranging from 0 to 7.
- **Grid Details**: The grid lines are in increments of 10 for \( N \) and 1 for \( S \).
### Solution:
To model the relationship, we use the given information:
- The company uses 1 cup of sugar for every 20 cookies.
This relationship can be expressed with a linear equation:
\[ S = \frac{1}{20}N \]
### Using the Graph:
- The graph will plot points that represent this equation. For example, when \( N = 20 \), \( S = 1 \); when \( N = 40 \), \( S = 2 \), and so on, creating a straight line through the origin (0,0) and the points calculated.
### Tools and Icons:
- **Rectangle and Options Box**: Represents drawing or graph control tools. The rectangle suggests a selection or drawing action, while the icons indicate different tool options such as rotation, undo, and additional help.
- **Equation Editing Tools**: Include icons for calculating, drawing, and a help option to assist in using graph tools to represent the equation visually.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F41328c37-5b30-4ef3-9d9d-bd85c249edfc%2Fcbc4da70-2a89-430f-ad97-b17a5c15ed29%2Fkeqyysa_processed.png&w=3840&q=75)
Transcribed Image Text:# Writing an Equation and Drawing Its Graph to Model a Real-World Scenario
### Problem Statement:
A cookie company uses one cup of sugar for every 20 cookies it makes.
Let \( S \) represent the total number of cups of sugar used, and let \( N \) represent the number of cookies made. Write an equation relating \( S \) to \( N \), and then graph the equation using the axes below.
### Explanation of the Graph:
- **Axes Overview**: The graph is a coordinate grid with the horizontal axis labeled \( N \) (representing the number of cookies) ranging from 0 to 110, and the vertical axis labeled \( S \) (representing the cups of sugar) ranging from 0 to 7.
- **Grid Details**: The grid lines are in increments of 10 for \( N \) and 1 for \( S \).
### Solution:
To model the relationship, we use the given information:
- The company uses 1 cup of sugar for every 20 cookies.
This relationship can be expressed with a linear equation:
\[ S = \frac{1}{20}N \]
### Using the Graph:
- The graph will plot points that represent this equation. For example, when \( N = 20 \), \( S = 1 \); when \( N = 40 \), \( S = 2 \), and so on, creating a straight line through the origin (0,0) and the points calculated.
### Tools and Icons:
- **Rectangle and Options Box**: Represents drawing or graph control tools. The rectangle suggests a selection or drawing action, while the icons indicate different tool options such as rotation, undo, and additional help.
- **Equation Editing Tools**: Include icons for calculating, drawing, and a help option to assist in using graph tools to represent the equation visually.
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