The Sum Of Three Numbers Is 45. The Second Of The Three Numbers Is Three More Than Twice The First Number, X X X . The Third Number Is Two More Than The First Number, X X X .Which Equation Can Be Used To Solve For The First Number,

Introduction

In mathematics, equations are used to represent relationships between variables. In this article, we will explore a problem involving three numbers, where the sum of the numbers is 45. The second number is three more than twice the first number, and the third number is two more than the first number. We will use algebraic expressions to represent these relationships and create an equation to solve for the first number.

The Problem

Let's denote the first number as $x$. According to the problem, the second number is three more than twice the first number, which can be represented as $2x + 3$. The third number is two more than the first number, which can be represented as $x + 2$.

Creating the Equation

We are given that the sum of the three numbers is 45. We can write an equation to represent this relationship:

$$x + (2x + 3) + (x + 2) = 45$$

Simplifying the Equation

To simplify the equation, we can combine like terms:

$$x + 2x + 3 + x + 2 = 45$$

$$4x + 5 = 45$$

Solving for $x$

To solve for $x$, we can subtract 5 from both sides of the equation:

$$4x = 40$$

Then, we can divide both sides of the equation by 4:

$$x = 10$$

Conclusion

In this article, we used algebraic expressions to represent the relationships between the three numbers. We created an equation to solve for the first number, $x$, and simplified the equation to find the value of $x$. The final answer is $x = 10$.

The Equation in Action

Let's use the equation to find the values of the second and third numbers:

• The second number is $2x + 3 = 2(10) + 3 = 23$
• The third number is $x + 2 = 10 + 2 = 12$

Real-World Applications

This type of problem can be applied to real-world situations, such as:

• Budgeting: If you have a total budget of $45 and you want to allocate it among three categories, you can use this equation to find the amount for each category.
• Resource allocation: If you have a limited resource, such as a certain number of hours to complete a project, and you want to allocate it among three tasks, you can use this equation to find the time for each task.

Final Thoughts

In conclusion, this article demonstrated how to create an equation to solve for the first number in a problem involving three numbers. We used algebraic expressions to represent the relationships between the numbers and simplified the equation to find the value of $x$. This type of problem can be applied to real-world situations, such as budgeting and resource allocation.

Additional Resources

• Algebraic Expressions
• Equations
• Mathematics

Related Articles

• The Sum of Two Numbers: A Mathematical Equation
• The Difference of Two Numbers: A Mathematical Equation

Tags

• Mathematics
• Algebra
• Equations
• Problem-solving
• Budgeting
• Resource allocation
  

Introduction

In our previous article, we explored a problem involving three numbers, where the sum of the numbers is 45. The second number is three more than twice the first number, and the third number is two more than the first number. We created an equation to solve for the first number, $x$. In this article, we will answer some frequently asked questions related to this problem.

Q&A

Q: What is the equation to solve for the first number, $x$?

A: The equation to solve for the first number, $x$, is:

$$x + (2x + 3) + (x + 2) = 45$$

Q: How do I simplify the equation?

A: To simplify the equation, you can combine like terms:

$$x + 2x + 3 + x + 2 = 45$$

$$4x + 5 = 45$$

Q: How do I solve for $x$?

A: To solve for $x$, you can subtract 5 from both sides of the equation:

$$4x = 40$$

Then, you can divide both sides of the equation by 4:

$$x = 10$$

Q: What are the values of the second and third numbers?

A: The second number is $2x + 3 = 2(10) + 3 = 23$

The third number is $x + 2 = 10 + 2 = 12$

Q: How can I apply this problem to real-world situations?

A: This type of problem can be applied to real-world situations, such as:

• Budgeting: If you have a total budget of $45 and you want to allocate it among three categories, you can use this equation to find the amount for each category.
• Resource allocation: If you have a limited resource, such as a certain number of hours to complete a project, and you want to allocate it among three tasks, you can use this equation to find the time for each task.

Q: What are some common mistakes to avoid when solving this problem?

A: Some common mistakes to avoid when solving this problem include:

• Not combining like terms
• Not subtracting 5 from both sides of the equation
• Not dividing both sides of the equation by 4

Q: How can I check my answer?

A: To check your answer, you can plug the value of $x$ back into the original equation:

$$x + (2x + 3) + (x + 2) = 45$$

$$10 + (2(10) + 3) + (10 + 2) = 45$$

$$10 + 23 + 12 = 45$$

$$45 = 45$$

This confirms that the value of $x$ is correct.

Conclusion

In this article, we answered some frequently asked questions related to the problem involving three numbers. We provided step-by-step solutions to the equation and discussed common mistakes to avoid. We also explored real-world applications of this problem and provided tips for checking your answer.

Additional Resources

• Algebraic Expressions
• Equations
• Mathematics

Related Articles

• The Sum of Two Numbers: A Mathematical Equation
• The Difference of Two Numbers: A Mathematical Equation

Tags

• Mathematics
• Algebra
• Equations
• Problem-solving
• Budgeting
• Resource allocation