Expressing Kojo's Share A Mathematical Problem With Kofi And Kojo

In this mathematical scenario, we delve into the distribution of money between two individuals, Kofi and Kojo. The core of the problem lies in deciphering how a sum of GH¢380.00 is divided between them, given that Kojo receives GH¢75.00 more than Kofi. To navigate this, we introduce a variable, x, to represent Kofi's share. This variable becomes our cornerstone, allowing us to build an expression that accurately reflects Kojo's portion of the total amount. The challenge here is not just to find the value of x, but to articulate Kojo's share in terms of x, laying the groundwork for solving the problem in its entirety. This involves a blend of algebraic thinking and a clear grasp of the relationships described in the problem statement. How do we translate the information about Kojo having GH¢75.00 more than Kofi into a mathematical expression? How does the total sum of GH¢380.00 fit into this equation? These are the questions we aim to answer, paving the way for a deeper understanding of proportional sharing and algebraic problem-solving techniques. This initial step is crucial, setting the stage for the subsequent calculations that will ultimately reveal the specific amounts each person receives. So, let's embark on this mathematical journey, unraveling the intricacies of the problem step by step, ensuring that every detail is meticulously considered and incorporated into our solution strategy.

Defining the Expression for Kojo's Share

To express Kojo's share mathematically, we build upon the foundation laid by defining Kofi's share as x. The problem explicitly states that Kojo has GH¢75.00 more than Kofi. In mathematical terms, this translates to adding GH¢75.00 to Kofi's share to find Kojo's share. Therefore, Kojo's share can be represented by the expression x + GH¢75.00. This expression is the heart of our solution, encapsulating the relationship between Kofi's and Kojo's portions of the total amount. It's a simple yet powerful algebraic representation that allows us to proceed with solving the problem. Understanding this expression is crucial because it forms the basis for setting up an equation that incorporates the total sum of GH¢380.00. Without accurately defining Kojo's share in terms of x, we would be unable to progress towards finding the specific values of their individual shares. The elegance of algebra lies in its ability to translate real-world scenarios into concise mathematical statements, and this expression perfectly exemplifies that. It's a testament to the power of variables and expressions in simplifying complex problems and making them amenable to mathematical manipulation. With this expression in hand, we are now equipped to take the next step: formulating an equation that captures the entirety of the problem's conditions and constraints. This will bring us closer to unraveling the numerical values that represent Kofi's and Kojo's respective shares.

Setting Up the Equation: Combining Shares to Reach the Total

Having defined both Kofi's share as x and Kojo's share as x + GH¢75.00, the next pivotal step is to formulate an equation that ties these expressions together with the total amount they share, which is GH¢380.00. The fundamental principle here is that the sum of Kofi's share and Kojo's share must equal the total amount. This can be expressed as an equation: x + (x + GH¢75.00) = GH¢380.00. This equation is the cornerstone of our solution, encapsulating the entire problem in a single, concise mathematical statement. It represents the balance between the individual shares and the collective total. By solving this equation, we can determine the value of x, which will then allow us to calculate both Kofi's and Kojo's shares. The equation highlights the power of algebra in translating real-world scenarios into symbolic representations that can be manipulated and solved. It's a testament to the ability of mathematics to capture the essence of a problem and provide a pathway to its solution. The equation is not just a collection of symbols; it's a narrative, telling the story of how the money is divided between Kofi and Kojo. It's a bridge connecting the abstract world of algebra to the concrete reality of financial transactions. With this equation in place, we are now poised to embark on the process of solving it, unraveling the mystery of how the GH¢380.00 is distributed between the two individuals. This algebraic journey will lead us to a clear and definitive answer, illuminating the specific amounts each person receives.

Solving for x: Determining Kofi's Share

To determine Kofi's share, represented by x, we must solve the equation we established: x + (x + GH¢75.00) = GH¢380.00. The first step in this process is to simplify the equation by combining like terms. This involves adding the x terms together, resulting in 2x + GH¢75.00 = GH¢380.00. This simplification makes the equation more manageable and brings us closer to isolating the variable x. The next step is to isolate the term containing x by subtracting GH¢75.00 from both sides of the equation. This maintains the balance of the equation while moving us closer to solving for x. Performing this subtraction yields 2x = GH¢380.00 - GH¢75.00, which simplifies to 2x = GH¢305.00. Now, to finally solve for x, we divide both sides of the equation by 2. This isolates x on one side of the equation and gives us its value. Performing this division gives us x = GH¢305.00 / 2, which results in x = GH¢152.50. Therefore, Kofi's share is GH¢152.50. This is a crucial milestone in our problem-solving journey, as we have now determined the value of x, which represents Kofi's portion of the total amount. With this value in hand, we can now easily calculate Kojo's share by substituting it into the expression we previously defined. This step demonstrates the power of algebraic manipulation in solving real-world problems, allowing us to systematically unravel the unknowns and arrive at a precise solution. The determination of Kofi's share is not just a numerical answer; it's a key piece of the puzzle that unlocks the entire solution, revealing the financial distribution between Kofi and Kojo.

Calculating Kojo's Share: Substituting the Value of x

Now that we have determined Kofi's share to be GH¢152.50, we can easily calculate Kojo's share using the expression we defined earlier: x + GH¢75.00. To do this, we simply substitute the value of x, which is GH¢152.50, into the expression. This gives us Kojo's share = GH¢152.50 + GH¢75.00. Performing this addition, we find that Kojo's share is GH¢227.50. This calculation is a direct application of the algebraic expression we formulated, demonstrating the power of mathematical representation in solving real-world problems. It's a testament to the elegance and efficiency of algebra, allowing us to move seamlessly from a symbolic representation to a concrete numerical answer. The determination of Kojo's share completes our problem-solving journey, providing us with a clear understanding of how the GH¢380.00 was divided between Kofi and Kojo. We now know that Kofi received GH¢152.50 and Kojo received GH¢227.50, which satisfies the condition that Kojo had GH¢75.00 more than Kofi. This final calculation underscores the interconnectedness of the problem's elements, highlighting how each piece of information plays a crucial role in arriving at the solution. The successful calculation of Kojo's share is not just an end in itself; it's a validation of our entire problem-solving approach, confirming the accuracy and consistency of our algebraic manipulations.

Verifying the Solution: Ensuring Accuracy and Consistency

To ensure the accuracy and consistency of our solution, it is crucial to verify that the calculated shares of Kofi and Kojo meet the conditions stated in the problem. We determined that Kofi's share is GH¢152.50 and Kojo's share is GH¢227.50. The first condition to verify is that the sum of their shares equals the total amount, which is GH¢380.00. Adding their shares together, we get GH¢152.50 + GH¢227.50 = GH¢380.00. This confirms that our solution satisfies the total amount constraint. The second condition to verify is that Kojo had GH¢75.00 more than Kofi. To check this, we subtract Kofi's share from Kojo's share: GH¢227.50 - GH¢152.50 = GH¢75.00. This confirms that Kojo indeed had GH¢75.00 more than Kofi, as stated in the problem. By verifying both conditions, we can confidently conclude that our solution is accurate and consistent with the problem's requirements. This step is an essential part of the problem-solving process, as it provides a final check to ensure that no errors were made along the way. It's a safeguard against mistakes and a confirmation of the validity of our algebraic manipulations. The verification process not only validates the solution but also reinforces our understanding of the problem and the relationships between its elements. It's a testament to the importance of meticulousness and attention to detail in mathematical problem-solving. With the solution verified, we can confidently present our findings, knowing that they accurately reflect the distribution of money between Kofi and Kojo.

Conclusion: Reflecting on the Problem-Solving Process

In conclusion, we have successfully navigated the problem of dividing GH¢380.00 between Kofi and Kojo, given the condition that Kojo received GH¢75.00 more than Kofi. Through a systematic approach involving algebraic representation, equation formulation, and solution verification, we determined that Kofi's share is GH¢152.50 and Kojo's share is GH¢227.50. This problem-solving journey highlights the power of algebra in translating real-world scenarios into mathematical models that can be manipulated and solved. It demonstrates the importance of defining variables, formulating equations, and verifying solutions to ensure accuracy and consistency. The process of solving this problem not only provides us with the specific amounts each person received but also reinforces our understanding of proportional sharing and algebraic problem-solving techniques. It showcases the interconnectedness of mathematical concepts and their applicability to everyday situations. The successful resolution of this problem is a testament to the effectiveness of a structured approach, emphasizing the value of breaking down complex problems into smaller, manageable steps. It also underscores the significance of clear communication and logical reasoning in conveying mathematical ideas. As we reflect on this problem-solving process, we gain valuable insights into the nature of mathematics and its ability to illuminate and solve a wide range of challenges. The satisfaction of arriving at a correct and verified solution is a reward in itself, motivating us to continue exploring the fascinating world of mathematics and its endless possibilities.