One Number Is Four Times As Large As Another Number, And Their Sum Is 505. What Are The Numbers?

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Introduction

Mathematics is a fascinating subject that involves solving various types of problems, including algebraic equations, geometric shapes, and number theory. In this article, we will delve into a mathematical puzzle that involves two numbers, where one number is four times as large as the other, and their sum is 505. We will use algebraic techniques to solve this problem and find the two numbers.

The Problem

Let's assume that the smaller number is represented by the variable x. Since the larger number is four times as large as the smaller number, it can be represented as 4x. The problem states that the sum of these two numbers is 505, which can be written as an equation:

x + 4x = 505

Simplifying the Equation

To simplify the equation, we can combine like terms by adding x and 4x. This results in:

5x = 505

Solving for x

To solve for x, we need to isolate the variable x on one side of the equation. We can do this by dividing both sides of the equation by 5:

x = 505 / 5

x = 101

Finding the Larger Number

Now that we have found the value of x, we can find the larger number by multiplying x by 4:

4x = 4(101)

4x = 404

Conclusion

In this article, we have solved a mathematical puzzle that involved two numbers, where one number is four times as large as the other, and their sum is 505. We used algebraic techniques to simplify the equation and solve for the smaller number, which was found to be 101. The larger number was then found by multiplying the smaller number by 4, resulting in 404. This problem demonstrates the importance of algebraic techniques in solving mathematical puzzles and equations.

Real-World Applications

This problem has real-world applications in various fields, including finance, economics, and engineering. For example, in finance, the problem can be used to represent the relationship between the principal and interest of a loan. In economics, the problem can be used to represent the relationship between the supply and demand of a product. In engineering, the problem can be used to represent the relationship between the input and output of a system.

Tips and Tricks

Here are some tips and tricks to help you solve this problem:

  • Use algebraic techniques to simplify the equation and solve for the variable.
  • Make sure to isolate the variable on one side of the equation.
  • Use the correct order of operations to evaluate the equation.
  • Check your answer by plugging it back into the original equation.

Additional Resources

If you are interested in learning more about algebra and mathematical puzzles, here are some additional resources:

  • Khan Academy: Algebra
  • Mathway: Algebra Solver
  • MIT OpenCourseWare: Algebra

Conclusion

In conclusion, this article has demonstrated the importance of algebraic techniques in solving mathematical puzzles and equations. The problem of finding two numbers, where one number is four times as large as the other, and their sum is 505, has been solved using algebraic techniques. The smaller number was found to be 101, and the larger number was found to be 404. This problem has real-world applications in various fields and can be used to represent the relationship between the principal and interest of a loan, the supply and demand of a product, and the input and output of a system.

Introduction

In our previous article, we solved a mathematical puzzle that involved two numbers, where one number is four times as large as the other, and their sum is 505. We used algebraic techniques to simplify the equation and solve for the smaller number, which was found to be 101. The larger number was then found by multiplying the smaller number by 4, resulting in 404. In this article, we will answer some frequently asked questions about this problem.

Q&A

Q: What is the relationship between the two numbers?

A: The relationship between the two numbers is that one number is four times as large as the other. This can be represented as x + 4x = 505, where x is the smaller number.

Q: How do I solve this problem?

A: To solve this problem, you can use algebraic techniques to simplify the equation and solve for the variable. You can start by combining like terms, then isolate the variable on one side of the equation.

Q: What is the value of the smaller number?

A: The value of the smaller number is 101.

Q: What is the value of the larger number?

A: The value of the larger number is 404.

Q: Can I use this problem in real-world applications?

A: Yes, this problem has real-world applications in various fields, including finance, economics, and engineering. For example, in finance, the problem can be used to represent the relationship between the principal and interest of a loan. In economics, the problem can be used to represent the relationship between the supply and demand of a product. In engineering, the problem can be used to represent the relationship between the input and output of a system.

Q: How do I check my answer?

A: To check your answer, you can plug it back into the original equation. If the equation holds true, then your answer is correct.

Q: What are some tips and tricks to help me solve this problem?

A: Here are some tips and tricks to help you solve this problem:

  • Use algebraic techniques to simplify the equation and solve for the variable.
  • Make sure to isolate the variable on one side of the equation.
  • Use the correct order of operations to evaluate the equation.
  • Check your answer by plugging it back into the original equation.

Q: What are some additional resources that I can use to learn more about algebra and mathematical puzzles?

A: Here are some additional resources that you can use to learn more about algebra and mathematical puzzles:

  • Khan Academy: Algebra
  • Mathway: Algebra Solver
  • MIT OpenCourseWare: Algebra

Conclusion

In conclusion, this article has answered some frequently asked questions about the mathematical puzzle of finding two numbers, where one number is four times as large as the other, and their sum is 505. We have provided tips and tricks to help you solve this problem, as well as additional resources that you can use to learn more about algebra and mathematical puzzles.

Frequently Asked Questions

Here are some frequently asked questions about this problem:

  • Q: What is the relationship between the two numbers? A: The relationship between the two numbers is that one number is four times as large as the other.
  • Q: How do I solve this problem? A: To solve this problem, you can use algebraic techniques to simplify the equation and solve for the variable.
  • Q: What is the value of the smaller number? A: The value of the smaller number is 101.
  • Q: What is the value of the larger number? A: The value of the larger number is 404.

Additional Resources

Here are some additional resources that you can use to learn more about algebra and mathematical puzzles:

  • Khan Academy: Algebra
  • Mathway: Algebra Solver
  • MIT OpenCourseWare: Algebra

Conclusion

In conclusion, this article has provided a comprehensive guide to solving the mathematical puzzle of finding two numbers, where one number is four times as large as the other, and their sum is 505. We have provided tips and tricks to help you solve this problem, as well as additional resources that you can use to learn more about algebra and mathematical puzzles.