The Sum Of Two Numbers Is 149 And The Difference Is 31, Find The Numbers

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Introduction

Mathematics is a fascinating subject that involves solving various problems and puzzles. In this article, we will explore a classic problem that involves finding two numbers based on their sum and difference. The problem states that the sum of two numbers is 149 and the difference is 31. We will use algebraic equations to solve this problem and find the two numbers.

Understanding the Problem

Let's break down the problem and understand what is being asked. We have two unknown numbers, which we can represent as x and y. The sum of these two numbers is 149, which can be represented as x + y = 149. The difference between these two numbers is 31, which can be represented as x - y = 31.

Using Algebraic Equations to Solve the Problem

To solve this problem, we can use algebraic equations. We have two equations:

  1. x + y = 149
  2. x - y = 31

We can solve these equations simultaneously to find the values of x and y.

Adding the Equations

Let's add the two equations to eliminate the variable y.

x + y = 149 x - y = 31

Adding the two equations, we get:

2x = 180

Solving for x

Now, we can solve for x by dividing both sides of the equation by 2.

x = 180 / 2 x = 90

Substituting x into One of the Original Equations

Now that we have found the value of x, we can substitute it into one of the original equations to find the value of y. Let's substitute x into the first equation:

x + y = 149 90 + y = 149

Solving for y

Now, we can solve for y by subtracting 90 from both sides of the equation.

y = 149 - 90 y = 59

Conclusion

In this article, we used algebraic equations to solve a classic problem that involved finding two numbers based on their sum and difference. We represented the two unknown numbers as x and y and used the equations x + y = 149 and x - y = 31 to solve for their values. By adding the two equations, we eliminated the variable y and solved for x. We then substituted x into one of the original equations to find the value of y. The final answer is x = 90 and y = 59.

The Importance of Algebraic Equations in Real-Life Scenarios

Algebraic equations are used in various real-life scenarios, such as:

  • Finance: Algebraic equations are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Algebraic equations are used to model the behavior of physical systems, such as the motion of objects and the behavior of electrical circuits.
  • Engineering: Algebraic equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Tips for Solving Algebraic Equations

Here are some tips for solving algebraic equations:

  • Read the problem carefully: Make sure you understand what is being asked and what the variables represent.
  • Use algebraic manipulations: Use addition, subtraction, multiplication, and division to simplify the equation and isolate the variable.
  • Check your work: Verify that your solution satisfies the original equation.

Conclusion

Introduction

In our previous article, we explored a classic problem that involved finding two numbers based on their sum and difference. We used algebraic equations to solve the problem and found the two numbers. In this article, we will answer some frequently asked questions related to the problem.

Q&A

Q: What is the sum of the two numbers?

A: The sum of the two numbers is 149.

Q: What is the difference between the two numbers?

A: The difference between the two numbers is 31.

Q: How did you solve the problem?

A: We used algebraic equations to solve the problem. We represented the two unknown numbers as x and y and used the equations x + y = 149 and x - y = 31 to solve for their values.

Q: Can you explain the steps you took to solve the problem?

A: Here are the steps we took to solve the problem:

  1. We added the two equations to eliminate the variable y.
  2. We solved for x by dividing both sides of the equation by 2.
  3. We substituted x into one of the original equations to find the value of y.

Q: What are some real-life scenarios where algebraic equations are used?

A: Algebraic equations are used in various real-life scenarios, such as:

  • Finance: Algebraic equations are used to calculate interest rates, investment returns, and other financial metrics.
  • Science: Algebraic equations are used to model the behavior of physical systems, such as the motion of objects and the behavior of electrical circuits.
  • Engineering: Algebraic equations are used to design and optimize systems, such as bridges, buildings, and electronic circuits.

Q: What are some tips for solving algebraic equations?

A: Here are some tips for solving algebraic equations:

  • Read the problem carefully: Make sure you understand what is being asked and what the variables represent.
  • Use algebraic manipulations: Use addition, subtraction, multiplication, and division to simplify the equation and isolate the variable.
  • Check your work: Verify that your solution satisfies the original equation.

Q: Can you provide more examples of algebraic equations?

A: Here are some more examples of algebraic equations:

  • 2x + 5 = 11
  • x - 3 = 7
  • 4x = 24

Q: How do I know if I have solved the equation correctly?

A: To verify that you have solved the equation correctly, you can:

  • Check if the solution satisfies the original equation.
  • Use a calculator to check if the solution is correct.
  • Ask a teacher or tutor to review your work.

Conclusion

In conclusion, algebraic equations are a powerful tool for solving problems in mathematics and other fields. By using algebraic equations, we can solve problems that involve unknown variables and relationships between them. We hope that this article has provided you with a better understanding of algebraic equations and how they can be used to solve real-life problems.

Additional Resources

For more information on algebraic equations, you can:

  • Visit the Khan Academy website, which provides a comprehensive introduction to algebraic equations.
  • Watch video tutorials on YouTube, such as 3Blue1Brown, which provides animated explanations of algebraic equations.
  • Consult a textbook or online resource, such as Mathway, which provides step-by-step solutions to algebraic equations.

Final Thoughts

Algebraic equations are a fundamental concept in mathematics and are used in various real-life scenarios. By understanding how to solve algebraic equations, you can develop problem-solving skills and apply them to a wide range of problems. We hope that this article has provided you with a better understanding of algebraic equations and how they can be used to solve real-life problems.