Solving For Ages Makayla, Kimberle, And Joni Math Problem

Unraveling age-related puzzles often requires a blend of careful reading, logical deduction, and the skillful application of algebraic principles. In this article, we embark on a mathematical journey to decipher the ages of three sisters: Makayla, Kimberle, and Joni. The challenge lies in translating the given information into a set of equations, which we will then solve to reveal the age of each sister. Let's delve into the problem, dissecting the clues and employing mathematical techniques to arrive at the solution.

Problem Statement: A Trio of Sisters and Their Ages

The core of our challenge lies in the following relationships between the sisters' ages:

1. Makayla is twice as old as Kimberle.
2. Joni is 3 years younger than Kimberle.
3. The sum of the sisters' ages is 57.

Our mission is to determine the age of each sister based on these three pieces of information. This is a classic algebraic problem where we can use variables to represent the unknowns (the sisters' ages) and form equations based on the given relationships. By solving these equations, we will uncover the ages of Makayla, Kimberle, and Joni.

Setting Up the Equations: Translating Words into Math

To solve this age puzzle, the first step is to translate the word statements into mathematical equations. This involves assigning variables to the unknown quantities, which in this case are the ages of the three sisters. Let's use the following variables:

• Let Makayla's age be represented by the variable M.
• Let Kimberle's age be represented by the variable K.
• Let Joni's age be represented by the variable J.

Now, we can rewrite the given information as equations:

1. "Makayla is twice as old as Kimberle" translates to the equation: M = 2K
2. "Joni is 3 years younger than Kimberle" translates to the equation: J = K - 3
3. "The sum of the sisters' ages is 57" translates to the equation: M + K + J = 57

With these three equations, we have a system of linear equations that we can solve to find the values of M, K, and J. The next step involves choosing a method to solve this system, such as substitution or elimination.

Solving the System of Equations: Unveiling the Ages

Now that we have our system of equations, we can use a method like substitution to solve for the ages of the sisters. Here are the equations we've established:

1. M = 2K
2. J = K - 3
3. M + K + J = 57

The substitution method involves solving one equation for one variable and then substituting that expression into another equation. Let's substitute equations (1) and (2) into equation (3):

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

Now we have an equation with only one variable, K. Let's simplify and solve for K:

4K - 3 = 57

Add 3 to both sides:

4K = 60

Divide both sides by 4:

K = 15

So, Kimberle is 15 years old. Now that we know K, we can find M and J using equations (1) and (2):

M = 2K = 2 * 15 = 30

J = K - 3 = 15 - 3 = 12

Therefore, Makayla is 30 years old and Joni is 12 years old. We have successfully determined the age of each sister using the power of algebra.

The Solution: Makayla, Kimberle, and Joni's Ages Revealed

After carefully setting up and solving the system of equations, we have arrived at the ages of the three sisters:

• Makayla is 30 years old.
• Kimberle is 15 years old.
• Joni is 12 years old.

These ages satisfy all the conditions given in the problem. Makayla is indeed twice as old as Kimberle (30 = 2 * 15), Joni is 3 years younger than Kimberle (12 = 15 - 3), and the sum of their ages is 57 (30 + 15 + 12 = 57). This solution demonstrates the power of algebra in solving real-world problems involving relationships between quantities.

Identifying the Equation Category: A Matter of Mathematics

The question "Identify which equation below fits the description of the word" clearly falls under the category of mathematics. This is because equations are fundamental mathematical tools used to represent relationships between quantities and solve problems. The question involves understanding the structure and meaning of equations, which is a core concept in mathematics.

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