Substituting the First Equation

Oct 13, 2025 by magicalceylontours.com 94 views

Introduction

In this article, we will delve into a mathematical puzzle involving two individuals, Adele and Timothy. The problem states that Adele is 5 years older than Timothy, and in three years, Timothy will be $\frac{2}{3}$ of Adele's age. Our goal is to determine Adele's current age.

Let's Break Down the Problem

To solve this problem, we need to set up an equation that represents the given information. Let's denote Adele's current age as $A$ and Timothy's current age as $T$ . We know that Adele is 5 years older than Timothy, so we can write an equation:

A = T + 5

We are also given that in three years, Timothy will be $\frac{2}{3}$ of Adele's age. This means that Timothy's age in three years will be $\frac{2}{3}$ of Adele's age in three years. We can represent this as:

T + 3 = \frac{2}{3}(A + 3)

Simplifying the Equation

Now that we have set up the equation, let's simplify it to make it easier to solve. We can start by multiplying both sides of the equation by 3 to eliminate the fraction:

3(T + 3) = 2(A + 3)

Expanding the left-hand side of the equation, we get:

3T + 9 = 2A + 6

Substituting the First Equation

We can substitute the first equation, $A = T + 5$ , into the simplified equation to eliminate the variable $A$ . We get:

3T + 9 = 2(T + 5) + 6

Expanding the right-hand side of the equation, we get:

3T + 9 = 2T + 10 + 6

Simplifying the equation further, we get:

3T + 9 = 2T + 16

Solving for T

Now that we have simplified the equation, let's solve for $T$ . We can start by subtracting $2T$ from both sides of the equation:

T + 9 = 16

Subtracting 9 from both sides of the equation, we get:

T = 7

Finding Adele's Current Age

Now that we have found Timothy's current age, we can use the first equation, $A = T + 5$ , to find Adele's current age. We get:

A = 7 + 5

Simplifying the equation, we get:

A = 12

Conclusion

In this article, we have solved a mathematical puzzle involving two individuals, Adele and Timothy. We have used algebraic equations to represent the given information and have solved for Adele's current age. The final answer is that Adele's current age is 12.

Additional Information

If you are interested in learning more about algebraic equations and how to solve them, we recommend checking out our article on Solving Linear Equations. This article provides a comprehensive guide to solving linear equations and includes examples and practice problems to help you improve your skills.

References

Comments

Introduction

In our previous article, we solved a mathematical puzzle involving two individuals, Adele and Timothy. We used algebraic equations to represent the given information and found that Adele's current age is 12. In this article, we will answer some of the most frequently asked questions about the puzzle.

Q: What is the relationship between Adele's and Timothy's ages?

A: Adele is 5 years older than Timothy.

Q: How do we know that in three years, Timothy will be $\frac{2}{3}$ of Adele's age?

A: This is given in the problem statement. We are told that in three years, Timothy's age will be $\frac{2}{3}$ of Adele's age in three years.

Q: How do we set up the equation to represent the given information?

A: We set up two equations:

$A = T + 5$ , which represents the relationship between Adele's and Timothy's ages.
$T + 3 = \frac{2}{3}(A + 3)$ , which represents the relationship between their ages in three years.

Q: How do we simplify the equation to make it easier to solve?

A: We multiply both sides of the equation by 3 to eliminate the fraction, and then expand and simplify the equation.

Q: How do we substitute the first equation into the simplified equation?

A: We substitute $A = T + 5$ into the simplified equation to eliminate the variable $A$ .

Q: How do we solve for T?

A: We subtract $2T$ from both sides of the equation, and then subtract 9 from both sides of the equation to solve for $T$ .

Q: How do we find Adele's current age?

A: We use the first equation, $A = T + 5$ , and substitute $T = 7$ to find Adele's current age.

Q: What is the final answer?

A: Adele's current age is 12.

Q: What are some additional resources for learning more about algebraic equations?

A: We recommend checking out our article on Solving Linear Equations for a comprehensive guide to solving linear equations.

Q: What are some related articles that you might find interesting?

A: We recommend checking out our articles on Mathematical Puzzles and Solving Linear Equations.

Conclusion

In this article, we have answered some of the most frequently asked questions about the mathematical puzzle involving Adele and Timothy. We hope that this Q&A article has been helpful in clarifying any confusion and providing additional insights into the solution.

Additional Information

References

Comments

We would love to hear your thoughts on this article. Do you have any questions or comments about the solution to the mathematical puzzle? Please feel free to leave a comment below.