The Story Behind the Yarn Blankets

Oct 13, 2025 by magicalceylontours.com 76 views

Introduction

In this article, we will delve into the world of mathematics and explore a real-life scenario involving yarn blankets. Ms. Hogan, a skilled craftswoman, used a certain number of balls of yarn to make a baby blanket for her nephew. She then used five times that amount to create a blanket for herself. The equation $5x = 15$ represents the relationship between the number of balls of yarn used for each blanket. In this article, we will complete the story and model it using the given equation.

The Story Behind the Yarn Blankets

Ms. Hogan is a talented craftswoman who loves making blankets for her loved ones. She has a nephew who is about to be born, and she wants to make a special baby blanket for him. She decides to use $x$ balls of yarn to make the baby blanket. After completing the baby blanket, she is left with some yarn, and she decides to use it to make a blanket for herself.

The Equation $5x = 15$

The equation $5x = 15$ represents the relationship between the number of balls of yarn used for each blanket. The equation states that the number of balls of yarn used for the blanket for Ms. Hogan is five times the number of balls of yarn used for the baby blanket. In other words, if Ms. Hogan used $x$ balls of yarn for the baby blanket, she used $5x$ balls of yarn for the blanket for herself.

Solving the Equation

To solve the equation $5x = 15$ , we need to isolate the variable $x$ . We can do this by dividing both sides of the equation by 5.

\frac{5x}{5} = \frac{15}{5}

This simplifies to:

x = 3

The Complete Story

Now that we have solved the equation, we can complete the story. Ms. Hogan used 3 balls of yarn to make the baby blanket for her nephew. She then used 5 times that amount, or $5 \times 3 = 15$ balls of yarn, to make a blanket for herself.

Conclusion

In this article, we have completed the story of Ms. Hogan and her yarn blankets. We have used the equation $5x = 15$ to model the relationship between the number of balls of yarn used for each blanket. By solving the equation, we have found that Ms. Hogan used 3 balls of yarn to make the baby blanket and 15 balls of yarn to make the blanket for herself. This article demonstrates the real-life application of mathematical equations and how they can be used to solve problems.

Real-Life Applications

The equation $5x = 15$ has many real-life applications. For example, it can be used to calculate the cost of materials for a project. If a project requires 5 times the amount of materials as another project, the cost of materials for the first project can be calculated by multiplying the cost of materials for the second project by 5.

Mathematical Concepts

The equation $5x = 15$ involves several mathematical concepts, including:

Multiplication: The equation involves the multiplication of 5 and x.
Division: The equation involves the division of both sides by 5.
Variables: The equation involves a variable, x, which represents the number of balls of yarn used for the baby blanket.

Tips and Tricks

When solving equations like $5x = 15$ , it's essential to follow the order of operations. This means that you should perform any calculations inside the parentheses first, followed by any exponents, then multiplication and division, and finally addition and subtraction.

Practice Problems

Here are a few practice problems to help you practice solving equations like $5x = 15$ :

$2x = 10$
$4x = 20$
$6x = 30$

Conclusion

Q: What is the equation $5x = 15$ used for?

A: The equation $5x = 15$ is used to model the relationship between the number of balls of yarn used for a baby blanket and the number of balls of yarn used for a blanket for Ms. Hogan.

Q: How do I solve the equation $5x = 15$ ?

A: To solve the equation $5x = 15$ , you need to isolate the variable x by dividing both sides of the equation by 5.

Q: What is the value of x in the equation $5x = 15$ ?

A: The value of x in the equation $5x = 15$ is 3.

Q: How many balls of yarn did Ms. Hogan use to make the baby blanket?

A: Ms. Hogan used 3 balls of yarn to make the baby blanket.

Q: How many balls of yarn did Ms. Hogan use to make the blanket for herself?

A: Ms. Hogan used 15 balls of yarn to make the blanket for herself.

Q: What is the relationship between the number of balls of yarn used for the baby blanket and the number of balls of yarn used for the blanket for Ms. Hogan?

A: The number of balls of yarn used for the blanket for Ms. Hogan is five times the number of balls of yarn used for the baby blanket.

Q: Can I use the equation $5x = 15$ to solve other problems?

A: Yes, you can use the equation $5x = 15$ to solve other problems that involve a relationship between two quantities that is five times as much.

Q: What are some real-life applications of the equation $5x = 15$ ?

A: Some real-life applications of the equation $5x = 15$ include calculating the cost of materials for a project, determining the number of items needed for a recipe, and solving problems involving proportions.

Q: What mathematical concepts are involved in solving the equation $5x = 15$ ?

A: The mathematical concepts involved in solving the equation $5x = 15$ include multiplication, division, and variables.

Q: How can I practice solving equations like $5x = 15$ ?

A: You can practice solving equations like $5x = 15$ by working on practice problems, such as $2x = 10$ , $4x = 20$ , and $6x = 30$ .

Q: What are some tips and tricks for solving equations like $5x = 15$ ?

A: Some tips and tricks for solving equations like $5x = 15$ include following the order of operations, checking your work, and using visual aids to help you understand the problem.

Conclusion

In this article, we have answered some frequently asked questions about the equation $5x = 15$ . We have discussed the equation's real-life applications, mathematical concepts, and tips and tricks for solving it. We have also provided practice problems and answers to help you practice solving equations like $5x = 15$ .