Choose The Correct Equation That Represents The Following Situation:Addison Is 4 Times As Old As Charlie. In 22 Years, Addison Will Be Twice As Old As Charlie. Which Equation Represents Their Ages In 22 Years?A. 4 X + 22 = 2 ( X + 22 4x + 22 = 2(x + 22 4 X + 22 = 2 ( X + 22 ] B.

Understanding the Problem

In this problem, we are given information about the ages of two individuals, Addison and Charlie. We are told that Addison is 4 times as old as Charlie, and in 22 years, Addison will be twice as old as Charlie. Our task is to choose the correct equation that represents their ages in 22 years.

Breaking Down the Information

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

• Addison is 4 times as old as Charlie. This can be represented as: Addison's age = 4 × Charlie's age
• In 22 years, Addison will be twice as old as Charlie. This can be represented as: Addison's age in 22 years = 2 × Charlie's age in 22 years

Representing the Information Mathematically

Let's represent the information mathematically using variables. Let x be Charlie's current age, and let A be Addison's current age.

• Addison's age = 4 × Charlie's age: A = 4x
• In 22 years, Addison's age = 2 × Charlie's age: A + 22 = 2(x + 22)

Choosing the Correct Equation

Now that we have represented the information mathematically, let's choose the correct equation that represents their ages in 22 years.

• Option A: $4x + 22 = 2(x + 22)$
• Option B: $4x + 22 = 2x + 44$

To choose the correct equation, let's analyze each option:

• Option A: $4x + 22 = 2(x + 22)$
  • Expanding the right-hand side: $4x + 22 = 2x + 44$
  • Simplifying the equation: $2x = 22$
  • Solving for x: $x = 11$
  • Addison's age in 22 years: $A + 22 = 4(11) + 22 = 66$
  • Charlie's age in 22 years: $x + 22 = 11 + 22 = 33$
  • Addison's age in 22 years is indeed twice Charlie's age in 22 years: $66 = 2(33)$
• Option B: $4x + 22 = 2x + 44$
  • Expanding the right-hand side: $4x + 22 = 2x + 44$
  • Simplifying the equation: $2x = 22$
  • Solving for x: $x = 11$
  • Addison's age in 22 years: $A + 22 = 4(11) + 22 = 66$
  • Charlie's age in 22 years: $x + 22 = 11 + 22 = 33$
  • Addison's age in 22 years is not twice Charlie's age in 22 years: $66 ≠ 2(33)$

Conclusion

Based on our analysis, we can conclude that the correct equation that represents their ages in 22 years is:

$4x + 22 = 2(x + 22)$

This equation accurately represents the information given in the problem and satisfies the condition that Addison's age in 22 years is twice Charlie's age in 22 years.

Additional Tips and Tricks

When solving problems like this, it's essential to:

• Read the problem carefully and understand the information given
• Represent the information mathematically using variables
• Analyze each option carefully and check if it satisfies the conditions given in the problem
• Simplify the equation and solve for the variables
• Check if the solution satisfies the conditions given in the problem

Frequently Asked Questions

In this article, we will answer some frequently asked questions about choosing the correct equation that represents a given situation.

Q: What is the first step in choosing the correct equation?

A: The first step in choosing the correct equation is to read the problem carefully and understand the information given. This includes identifying the variables, the relationships between them, and the conditions that must be satisfied.

Q: How do I represent the information mathematically using variables?

A: To represent the information mathematically using variables, you need to identify the variables and assign them a value. For example, if the problem states that Addison is 4 times as old as Charlie, you can represent this as: A = 4x, where A is Addison's age and x is Charlie's age.

Q: How do I analyze each option carefully and check if it satisfies the conditions given in the problem?

A: To analyze each option carefully and check if it satisfies the conditions given in the problem, you need to:

• Expand the right-hand side of the equation
• Simplify the equation
• Solve for the variables
• Check if the solution satisfies the conditions given in the problem

Q: What are some common mistakes to avoid when choosing the correct equation?

A: Some common mistakes to avoid when choosing the correct equation include:

• Not reading the problem carefully and understanding the information given
• Not representing the information mathematically using variables
• Not analyzing each option carefully and checking if it satisfies the conditions given in the problem
• Not simplifying the equation and solving for the variables
• Not checking if the solution satisfies the conditions given in the problem

Q: How can I improve my problem-solving skills and become more confident in my ability to choose the correct equation?

A: To improve your problem-solving skills and become more confident in your ability to choose the correct equation, you can:

• Practice solving problems regularly
• Review and practice different types of problems
• Seek help from a teacher or tutor if you are struggling with a particular concept
• Join a study group or online community to discuss problems and share solutions
• Take your time and read the problem carefully before starting to solve it

Q: What are some real-world applications of choosing the correct equation?

A: Choosing the correct equation has many real-world applications, including:

• Science: Choosing the correct equation is essential in scientific research, where scientists use mathematical models to describe and predict natural phenomena.
• Engineering: Choosing the correct equation is critical in engineering, where engineers use mathematical models to design and optimize systems.
• Economics: Choosing the correct equation is essential in economics, where economists use mathematical models to analyze and predict economic trends.
• Finance: Choosing the correct equation is critical in finance, where financial analysts use mathematical models to analyze and predict financial trends.

Conclusion

Choosing the correct equation is an essential skill in mathematics and has many real-world applications. By following the tips and tricks outlined in this article, you can improve your problem-solving skills and become more confident in your ability to choose the correct equation. Remember to practice regularly, review and practice different types of problems, and seek help from a teacher or tutor if you are struggling with a particular concept.