Calculate Salary After Expenses Mummy's Financial Puzzle
Understanding financial management is crucial, and this mathematical problem allows us to explore how one allocates their income. Let's dive into the intricacies of this problem, involving mummy's salary allocation for rent and food, to determine her initial income. This article aims to provide a detailed, step-by-step explanation to solve this problem, making it accessible to everyone, whether you're a student, a parent helping with homework, or simply someone who enjoys a good mathematical puzzle. Understanding the fundamentals of percentage calculations and fractions is key to unraveling this scenario. We'll break down the problem into manageable parts, ensuring each step is clear and logical. This isn't just about finding the answer; it's about understanding the process and applying these principles to real-life financial situations. By the end of this article, you'll not only be able to solve this particular problem but also gain confidence in tackling similar financial math challenges. Let's embark on this mathematical journey together and decode mummy's salary!
Problem Statement
The problem states that a mummy spent 30% of her salary on rent and one-third of the remaining amount on food. After these expenses, she was left with $4200. The objective is to find out what her total salary was. This is a classic problem that combines percentage calculations and fractions, requiring us to work backward from the final amount to the original salary. To effectively solve this, we need to understand how each expense affects the remaining amount and then reverse these steps to find the initial salary. This involves setting up equations or using a step-by-step approach to trace back the money spent on food and rent. The problem is designed to test our understanding of financial management concepts and our ability to apply mathematical principles in practical scenarios. Therefore, a clear, methodical approach is essential to ensure accuracy and comprehension.
Breaking Down the Problem
To solve this problem effectively, it's crucial to break it down into smaller, more manageable steps. First, we identify the key information: Mummy spent 30% of her salary on rent, then one-third of the remainder on food, and finally, she had $4200 left. We need to work backward, focusing on what happened last. The $4200 represents the amount left after paying for food, which was one-third of the remaining amount after paying rent. This means that the $4200 is the result of the remaining two-thirds. Understanding this relationship is crucial for calculating the amount spent on food and the amount remaining after rent. Next, we need to factor in the rent, which was 30% of the total salary. This means the amount remaining after paying rent is 70% of her salary. By breaking down the problem this way, we can create a clear pathway to solve for the unknown salary. Each step builds upon the previous one, making the solution more accessible and less daunting.
Solving for the Amount Remaining After Rent
Let's focus on finding the amount remaining after mummy paid her rent. We know that the $4200 represents the amount she had left after spending one-third of the remainder on food. This means that $4200 is two-thirds (2/3) of the amount remaining after rent. To find the full amount remaining after rent (which we'll call "R"), we can set up the equation (2/3) * R = $4200. Solving for R involves multiplying both sides of the equation by the reciprocal of 2/3, which is 3/2. So, R = $4200 * (3/2). This calculation will give us the amount of money mummy had after paying rent but before paying for food. This step is crucial because it bridges the gap between the final amount and the initial salary. It allows us to isolate the impact of the rent payment, setting the stage for calculating the total salary. This careful, methodical approach ensures accuracy and clarity in our solution.
Calculating the Total Salary
Now that we know the amount remaining after rent, we can calculate mummy's total salary. Let's call the total salary "S." We know that the amount remaining after rent is 70% (or 0.7) of the total salary because she spent 30% on rent. From the previous step, we calculated the amount remaining after rent to be $4200 * (3/2), which equals $6300. So, we can set up the equation 0.7 * S = $6300. To solve for S, we divide both sides of the equation by 0.7. Therefore, S = $6300 / 0.7. This calculation will give us mummy's total salary before any expenses. This step is the culmination of our problem-solving process, bringing together the information we've gathered and the calculations we've performed. By carefully tracing back the expenses, we arrive at the initial salary, providing a comprehensive solution to the problem.
Solution
Let's finalize our calculations to find the solution. We previously established that the total salary, S, can be found by dividing $6300 by 0.7. Performing this division, we get S = $6300 / 0.7 = $9000. Therefore, mummy's total salary was $9000. This result answers the original question posed in the problem. To summarize, we first worked backward from the $4200 remaining after food expenses to find the amount remaining after rent, which was $6300. Then, using the fact that the rent was 30% of the salary, we determined that $6300 represents 70% of the salary. Finally, we calculated the total salary by dividing $6300 by 0.7. This step-by-step approach not only provides the answer but also reinforces the process of solving such financial math problems. Understanding each step is crucial for applying these skills in various real-life scenarios.
Verification
To ensure our solution is correct, it's essential to verify it. We found that mummy's salary was $9000. Let's retrace the steps: she spent 30% on rent, which is 0.3 * $9000 = $2700. This leaves her with $9000 - $2700 = $6300. Next, she spent one-third of the remainder on food, which is (1/3) * $6300 = $2100. Subtracting the food expenses, she has $6300 - $2100 = $4200 left. This matches the amount stated in the problem, confirming our solution. Verification is a critical step in problem-solving, ensuring accuracy and building confidence in our results. It involves retracing the steps using the calculated answer to see if it aligns with the given information. This process not only validates the solution but also reinforces understanding of the problem and the method used to solve it. By verifying our answer, we can confidently say that mummy's salary was indeed $9000.
Conclusion
In conclusion, we successfully solved the problem by carefully breaking it down into manageable steps and working backward from the final amount. We determined that mummy's total salary was $9000. This problem highlights the importance of understanding percentage calculations and fractions in financial management. The key to solving such problems lies in identifying the relationships between the different amounts and using a methodical approach to trace back the expenses. By breaking the problem into smaller parts, we made it easier to understand and solve. The verification step further solidified our confidence in the solution. This exercise not only enhances our mathematical skills but also provides valuable insights into real-life financial scenarios. Understanding how income is allocated and managed is crucial for financial literacy, and this problem serves as a practical example of applying mathematical concepts in everyday life. Remember, practice and a clear understanding of the underlying principles are essential for mastering problem-solving in mathematics and beyond.
