Representing the Problem Algebraically

Oct 13, 2025 by windailys.com 66 views

Introduction

Jonathan, a postcard and stamp enthusiast, has a vast collection of these items. His collection consists of postcards and stamps, with the number of postcards being 12 more than $\frac{3}{4}$ the number of stamps. We are given that Jonathan has a total of 39 postcards in his collection. The problem requires us to find the number of stamps Jonathan has, denoted by $x$ . To solve this problem, we will use algebraic equations to represent the given information and then solve for the unknown variable $x$ .

Understanding the Problem

Let's break down the information provided in the problem:

The number of postcards in Jonathan's collection is 12 more than $\frac{3}{4}$ the number of stamps.
Jonathan has 39 postcards in all.
We need to find the number of stamps Jonathan has, denoted by $x$ .

Representing the Problem Algebraically

To represent the problem algebraically, we can start by writing an equation that represents the relationship between the number of postcards and the number of stamps. Let's denote the number of stamps as $x$ . The number of postcards is 12 more than $\frac{3}{4}$ the number of stamps, which can be represented as:

\text{Number of postcards} = \frac{3}{4}x + 12

We are given that Jonathan has 39 postcards in all, so we can set up the equation:

\frac{3}{4}x + 12 = 39

Solving the Equation

To solve the equation, we can start by subtracting 12 from both sides of the equation:

\frac{3}{4}x = 27

Next, we can multiply both sides of the equation by $\frac{4}{3}$ to isolate $x$ :

x = 27 \times \frac{4}{3}

x = 36

Therefore, Jonathan has 36 stamps in his collection.

Conclusion

In this problem, we used algebraic equations to represent the relationship between the number of postcards and the number of stamps. We then solved the equation to find the number of stamps Jonathan has. This problem demonstrates the importance of using algebraic equations to represent real-world problems and solve for unknown variables.

Real-World Applications

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

Mathematics: This problem demonstrates the use of algebraic equations to solve real-world problems.
Statistics: This problem can be used to teach students about the concept of proportions and how to use them to solve problems.
Data Analysis: This problem can be used to teach students how to analyze data and make predictions based on that data.

Tips and Tricks

Use algebraic equations to represent real-world problems: This problem demonstrates the importance of using algebraic equations to represent real-world problems.
Solve equations step-by-step: To solve the equation, we need to follow the order of operations and solve the equation step-by-step.
Check your work: After solving the equation, we need to check our work to ensure that the solution is correct.

Frequently Asked Questions

What is the number of stamps Jonathan has? Jonathan has 36 stamps in his collection.
How do we represent the problem algebraically? We can represent the problem algebraically by writing an equation that represents the relationship between the number of postcards and the number of stamps.
How do we solve the equation? We can solve the equation by following the order of operations and solving the equation step-by-step.

Introduction

In our previous article, we solved the postcard and stamp problem using algebraic equations. In this article, we will provide a Q&A section to help readers understand the problem and its solution better. We will answer some frequently asked questions related to the problem and provide additional information to help readers grasp the concept.

Q&A Section

Q: What is the number of stamps Jonathan has?

A: Jonathan has 36 stamps in his collection.

Q: How do we represent the problem algebraically?

A: We can represent the problem algebraically by writing an equation that represents the relationship between the number of postcards and the number of stamps. In this case, the equation is:

\frac{3}{4}x + 12 = 39

Q: How do we solve the equation?

A: We can solve the equation by following the order of operations and solving the equation step-by-step. First, we subtract 12 from both sides of the equation:

\frac{3}{4}x = 27

Next, we multiply both sides of the equation by $\frac{4}{3}$ to isolate $x$ :

x = 27 \times \frac{4}{3}

x = 36

Q: What is the significance of the $\frac{3}{4}$ term in the equation?

A: The $\frac{3}{4}$ term in the equation represents the proportion of stamps that Jonathan has. In this case, Jonathan has $\frac{3}{4}$ of the stamps that he has postcards.

Q: How can we use this problem to teach students about proportions?

A: This problem can be used to teach students about proportions by showing them how to represent a real-world problem using algebraic equations. Students can learn how to use proportions to solve problems and make predictions based on that data.

Q: What are some real-world applications of this problem?

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

Mathematics: This problem demonstrates the use of algebraic equations to solve real-world problems.
Statistics: This problem can be used to teach students about the concept of proportions and how to use them to solve problems.
Data Analysis: This problem can be used to teach students how to analyze data and make predictions based on that data.

Additional Tips and Tricks

Use algebraic equations to represent real-world problems: This problem demonstrates the importance of using algebraic equations to represent real-world problems.
Solve equations step-by-step: To solve the equation, we need to follow the order of operations and solve the equation step-by-step.
Check your work: After solving the equation, we need to check our work to ensure that the solution is correct.

Conclusion

In this Q&A article, we provided answers to some frequently asked questions related to the postcard and stamp problem. We also provided additional information to help readers understand the problem and its solution better. We hope that this article has been helpful in clarifying any doubts that readers may have had.

Frequently Asked Questions

What is the number of stamps Jonathan has? Jonathan has 36 stamps in his collection.
How do we represent the problem algebraically? We can represent the problem algebraically by writing an equation that represents the relationship between the number of postcards and the number of stamps.
How do we solve the equation? We can solve the equation by following the order of operations and solving the equation step-by-step.

Solving the Postcard and Stamp Problem: An Equation-Based Approach
Mathematics: A Real-World Approach
Statistics: A Data-Driven Approach

Resources

Algebraic Equations: A Guide to Solving Real-World Problems
Proportions: A Guide to Understanding and Solving Problems
Data Analysis: A Guide to Analyzing and Making Predictions