Solving Age Word Problem Makayla Kimberle Joni

In the realm of mathematical puzzles, age-related problems often present intriguing challenges. This article delves into a classic age problem involving three sisters – Makayla, Kimberle, and Joni – where their ages are interconnected through a series of clues. We will embark on a step-by-step journey, unraveling the relationships between their ages, formulating equations, and ultimately discovering the age of each sister. Our primary goal is to transform this word problem into a clear mathematical equation and solve it effectively. This process will not only demonstrate problem-solving techniques but also emphasize the importance of translating real-world scenarios into mathematical models.

Unraveling the Age Puzzle: Makayla, Kimberle, and Joni

Let's begin by carefully examining the information provided in the problem statement. We know that Makayla is twice as old as Kimberle. This key relationship establishes a direct link between their ages. Next, we learn that Joni is 3 years younger than Kimberle, introducing another crucial piece of the puzzle. Finally, we are given the sum of the sisters' ages, which is 57. This final piece of information will serve as the cornerstone for our equation.

To effectively tackle this problem, we need to translate these verbal relationships into mathematical expressions. Let's represent Kimberle's age with the variable x. Since Makayla is twice as old as Kimberle, Makayla's age can be expressed as 2x. Similarly, as Joni is 3 years younger than Kimberle, Joni's age can be represented as x - 3. Now, we have successfully transformed the verbal clues into algebraic expressions, setting the stage for the next step: formulating the equation.

Formulating the Equation: Bridging Words and Math

With the ages of Makayla, Kimberle, and Joni represented in terms of x, we can now construct an equation that captures the essence of the problem. We know that the sum of their ages is 57. Therefore, we can write the equation as:

2x + x + (x - 3) = 57

This equation beautifully encapsulates the relationships between the sisters' ages and their combined total. It is the bridge that connects the word problem to the world of mathematics, allowing us to employ algebraic techniques to find the solution. The equation showcases the power of mathematical representation in simplifying complex scenarios and making them amenable to analysis.

Solving the Equation: A Step-by-Step Approach

Now that we have our equation, the next step is to solve it for x, which represents Kimberle's age. Let's break down the process step by step:

1. Combine like terms: 2x + x + x - 3 = 4x - 3
2. Rewrite the equation: 4x - 3 = 57
3. Add 3 to both sides: 4x = 60
4. Divide both sides by 4: x = 15

Therefore, Kimberle's age is 15 years old. This is a significant milestone in our problem-solving journey. We have successfully determined the value of x, which is the foundation for finding the ages of the other sisters. The methodical approach we employed, combining like terms, isolating the variable, and performing inverse operations, exemplifies the core principles of algebraic problem-solving.

Determining the Ages: Unveiling the Sisters' Secrets

With Kimberle's age (x) determined to be 15, we can now easily find the ages of Makayla and Joni. Makayla's age is 2x, so Makayla is 2 * 15 = 30 years old. Joni's age is x - 3, so Joni is 15 - 3 = 12 years old.

Therefore, the ages of the sisters are: Makayla is 30 years old, Kimberle is 15 years old, and Joni is 12 years old. We have successfully solved the age problem, unraveling the intricate relationships between the sisters' ages. This solution not only answers the specific question posed but also highlights the power of algebraic thinking in solving real-world problems.

Identifying the Correct Equation: A Multiple-Choice Challenge

Now, let's address the final part of the problem: identifying the equation that accurately represents the given word problem from the options provided. The options are:

A. (2 + x) + (x - 3) = 57 B. [The problem does not provide option B.]

Our derived equation is 2x + x + (x - 3) = 57. Let's analyze each option and see if it matches our equation. Option A, (2 + x) + (x - 3) = 57, is clearly different from our equation. It does not correctly represent the relationship that Makayla is twice as old as Kimberle, instead adding a constant 2 to x. Therefore, Option A is incorrect.

The Correct Equation Unveiled

To determine the correct equation, it's crucial to revisit the problem statement and carefully translate the verbal clues into mathematical expressions. Kimberle's age is represented by x, Makayla's age is twice Kimberle's age (2x), and Joni's age is 3 years younger than Kimberle's age (x - 3). The sum of their ages is 57. Therefore, the correct equation should be:

2x + x + (x - 3) = 57

This equation accurately reflects the relationships between the sisters' ages and their combined total. It captures the essence of the word problem and allows us to solve for the unknown variable, x. This exercise underscores the importance of meticulous attention to detail and accurate translation of verbal information into mathematical form.

Conclusion: The Power of Mathematical Problem-Solving

In conclusion, we have successfully navigated the age puzzle involving Makayla, Kimberle, and Joni. We translated the word problem into a mathematical equation, solved for the unknown variable, and determined the age of each sister. Through this process, we have demonstrated the power of algebraic thinking in unraveling real-world problems. The ability to represent relationships mathematically, formulate equations, and solve them systematically is a valuable skill that extends far beyond the realm of mathematics.

This problem highlights the importance of carefully reading and understanding the problem statement, identifying key relationships, and translating them into mathematical expressions. The step-by-step approach we employed, from formulating the equation to solving it and verifying the solution, is a testament to the power of structured problem-solving. Mathematical problem-solving is not just about finding the right answer; it's about developing critical thinking skills, logical reasoning, and the ability to approach challenges with confidence and precision.

This article has not only provided a solution to a specific age problem but has also offered insights into the broader application of mathematical principles in everyday life. The ability to translate real-world scenarios into mathematical models is a valuable asset in various fields, from science and engineering to finance and economics. By mastering the art of mathematical problem-solving, we empower ourselves to tackle challenges, make informed decisions, and navigate the complexities of the world around us.