Possible Numbers of Meters of Fabric

Oct 13, 2025 by vinooalluri.com 124 views

Introduction

In this article, we will delve into a mathematical problem that involves inequalities and algebraic expressions. We will explore the possible numbers of meters of fabric David will buy, given that he will spend at least $20 and the fabric costs $2 per meter. Our goal is to write an inequality that can be used to find the number of meters of fabric David will buy.

The Problem

David will spend at least $20 buying fabric. The fabric costs $2 per meter. Let's look at the possible numbers of meters of fabric David will buy.

Step 1: Define the Variables

Let's define the variable x as the number of meters of fabric David will buy. We are given that the fabric costs $2 per meter, so the total cost of the fabric will be 2x dollars.

Step 2: Write the Inequality

Since David will spend at least $20, we can write an inequality to represent this situation:

2x ≥ 20

This inequality states that the total cost of the fabric (2x) is greater than or equal to $20.

Step 3: Solve the Inequality

To solve the inequality, we can divide both sides by 2:

x ≥ 10

This means that the number of meters of fabric David will buy (x) is greater than or equal to 10.

Conclusion

In this article, we explored a mathematical problem that involved inequalities and algebraic expressions. We defined the variable x as the number of meters of fabric David will buy and wrote an inequality to represent the situation. We then solved the inequality to find the possible numbers of meters of fabric David will buy. The solution to the inequality is x ≥ 10, which means that David will buy at least 10 meters of fabric.

Possible Numbers of Meters of Fabric

Now that we have the inequality x ≥ 10, we can find the possible numbers of meters of fabric David will buy. Since x represents the number of meters of fabric, we can list the possible values of x:

10 meters
11 meters
12 meters
13 meters
14 meters
15 meters
16 meters
17 meters
18 meters
19 meters
20 meters

Graphical Representation

We can also represent the inequality x ≥ 10 graphically. The graph of the inequality will be a line that represents the equation x = 10. The region above the line will represent the possible values of x.

Real-World Applications

This problem has real-world applications in various fields, such as:

Business: A company may need to buy a certain amount of fabric to produce a product. The company may want to know the minimum amount of fabric they need to buy to meet their production requirements.
Engineering: An engineer may need to design a system that requires a certain amount of fabric. The engineer may want to know the minimum amount of fabric they need to design the system.
Science: A scientist may need to conduct an experiment that requires a certain amount of fabric. The scientist may want to know the minimum amount of fabric they need to conduct the experiment.

Conclusion

Introduction

In our previous article, we explored a mathematical problem that involved inequalities and algebraic expressions. We defined the variable x as the number of meters of fabric David will buy and wrote an inequality to represent the situation. We then solved the inequality to find the possible numbers of meters of fabric David will buy. In this article, we will answer some frequently asked questions related to David's fabric purchase.

Q&A

Q: What is the minimum amount of fabric David will buy?

A: According to the inequality x ≥ 10, the minimum amount of fabric David will buy is 10 meters.

Q: What is the maximum amount of fabric David will buy?

A: Since there is no upper bound on the inequality x ≥ 10, the maximum amount of fabric David will buy is infinite. However, in reality, David will only buy a finite amount of fabric.

Q: How much will David spend on fabric if he buys 10 meters?

A: If David buys 10 meters of fabric, he will spend 2x = 2(10) = $20.

Q: How much will David spend on fabric if he buys 20 meters?

A: If David buys 20 meters of fabric, he will spend 2x = 2(20) = $40.

Q: What if the fabric costs $3 per meter instead of $2 per meter?

A: If the fabric costs $3 per meter, the inequality will change to 3x ≥ 20. Solving for x, we get x ≥ 20/3 ≈ 6.67 meters.

Q: What if David wants to buy fabric that costs $1.50 per meter?

A: If the fabric costs $1.50 per meter, the inequality will change to 1.5x ≥ 20. Solving for x, we get x ≥ 20/1.5 = 13.33 meters.

Q: Can David buy fabric that costs $2 per meter and spend less than $20?

A: No, according to the inequality x ≥ 10, David will spend at least $20 on fabric that costs $2 per meter.

Q: Can David buy fabric that costs $2 per meter and spend more than $20?

A: Yes, according to the inequality x ≥ 10, David can buy more than 10 meters of fabric that costs $2 per meter and spend more than $20.

Conclusion

In conclusion, this article answered some frequently asked questions related to David's fabric purchase. We explored the minimum and maximum amounts of fabric David will buy, how much he will spend on fabric for different amounts, and what happens if the fabric costs a different price per meter. We hope this article has been helpful in understanding the problem and its solutions.

Real-World Applications

This problem has real-world applications in various fields, such as:

Business: A company may need to buy a certain amount of fabric to produce a product. The company may want to know the minimum amount of fabric they need to buy to meet their production requirements.
Engineering: An engineer may need to design a system that requires a certain amount of fabric. The engineer may want to know the minimum amount of fabric they need to design the system.
Science: A scientist may need to conduct an experiment that requires a certain amount of fabric. The scientist may want to know the minimum amount of fabric they need to conduct the experiment.

Tips and Tricks

When solving inequalities, make sure to consider both the greater than or equal to (≥) and less than or equal to (≤) symbols.
When solving inequalities, make sure to consider the direction of the inequality (i.e., whether the inequality is pointing up or down).
When solving inequalities, make sure to consider the units of the variables (i.e., whether the variables are measured in meters, feet, inches, etc.).

Conclusion

In conclusion, this article has provided a comprehensive guide to David's fabric purchase. We have explored the problem and its solutions, answered frequently asked questions, and provided real-world applications and tips and tricks. We hope this article has been helpful in understanding the problem and its solutions.