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.

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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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.
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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