Amina And Brody's Bonus Calculating Spending Differences

In this article, we'll delve into a practical mathematical problem involving percentages and fractions, focusing on how to calculate and compare expenditures. The scenario presents Amina and Brody, both recipients of a $£600$ bonus, and explores the differences in their spending habits. Amina spends $8\%$ of her bonus, while Brody spends $\frac{1}{20}$ of his. Our goal is to determine precisely how much more Amina spends compared to Brody. This exercise is not just about crunching numbers; it’s about understanding how to apply mathematical concepts to real-life situations, enhancing our ability to manage finances and make informed decisions. Through this detailed exploration, we aim to clarify the steps involved in percentage and fraction calculations, providing a comprehensive understanding that can be applied to similar problems in the future.

Before diving into the calculations, it’s crucial to fully understand the problem. Amina and Brody each start with a bonus of $£600$. Amina's spending is given as a percentage, $8\%$, while Brody's spending is given as a fraction, $\frac{1}{20}$. The core of the problem lies in converting these different representations into actual monetary values and then comparing them. To effectively solve this, we need to know how to calculate a percentage of a given amount and how to find a fractional part of a whole. Understanding these fundamental concepts is key to accurately determining the difference in their spending. The problem highlights the practical application of mathematical skills in everyday financial scenarios, making it a valuable exercise in both arithmetic and financial literacy. The challenge is not just to find the numbers, but to understand the proportional relationships they represent.

To determine how much Amina spends, we need to calculate $8\%$ of her $£600$ bonus. A percentage is essentially a fraction out of 100, so $8\%$ can be written as $\frac{8}{100}$. To find $8\%$ of $£600$, we multiply the fraction by the total amount. Mathematically, this looks like: $(\frac{8}{100}) imes 600$. This calculation involves multiplying 8 by 600 and then dividing by 100. Alternatively, we can simplify the calculation by first dividing 600 by 100, which gives us 6, and then multiplying 8 by 6. This simplified approach often makes mental calculations easier. The result of this calculation will give us the exact amount Amina spent from her bonus. Understanding how to convert percentages to fractions and perform these calculations is a fundamental skill in mathematics and is particularly useful in various real-life situations, such as calculating discounts, interest rates, and taxes. In this specific scenario, the accurate calculation of Amina's spending is a critical step towards solving the overall problem of comparing her spending to Brody's.

Next, we need to calculate how much Brody spends, which is $\frac{1}{20}$ of his $£600$ bonus. To find a fraction of a whole, we multiply the fraction by the total amount. In this case, we multiply $\frac{1}{20}$ by $£600$. This can be written as $(\frac{1}{20}) imes 600$. This calculation involves dividing 600 by 20. To make this division simpler, we can think of it as how many times 20 fits into 600. Another way to approach this is to divide 60 by 2, since 600 is just 60 with an additional zero. The result of this division will give us the amount Brody spent. This calculation highlights the practical application of fractions in real-world scenarios, particularly in situations involving sharing, dividing, or calculating portions of a whole. Understanding how to perform these fractional calculations is essential for various mathematical problems and everyday tasks, such as cooking, measuring, and financial planning. In the context of our problem, accurately determining Brody's spending is crucial for comparing it with Amina's and finding the difference between their expenditures.

After calculating how much Amina and Brody each spent, the next step is to compare their spending amounts. This involves finding the difference between the two amounts. To do this, we subtract the smaller amount from the larger amount. If Amina spent $A$ pounds and Brody spent $B$ pounds, and $A$ is greater than $B$, then the difference in their spending is $A - B$. This subtraction will give us the exact amount by which Amina's spending exceeds Brody's spending. This step is crucial for answering the main question of the problem, which is to determine how much more Amina spent than Brody. The comparison not only provides a numerical answer but also offers insights into the relative spending habits of Amina and Brody. Understanding how to compare quantities and find differences is a fundamental skill in mathematics and is widely applicable in various contexts, such as comparing prices, distances, or scores. In this specific scenario, the accurate comparison of their spending amounts is the key to solving the problem and drawing a meaningful conclusion.

1. Calculate Amina's spending: Amina spends $8\%$ of $£600$. To find this, we calculate $(\frac{8}{100}) imes 600$. This equals $48$. So, Amina spends $£48$.
2. Calculate Brody's spending: Brody spends $\frac{1}{20}$ of $£600$. To find this, we calculate $(\frac{1}{20}) imes 600$. This equals $30$. So, Brody spends $£30$.
3. Compare their spending: To find how much more Amina spends than Brody, we subtract Brody's spending from Amina's spending: $£48 - £30 = £18$.

Therefore, Amina spends $£18$ more than Brody. This final answer provides a clear and concise solution to the problem, highlighting the difference in their spending habits. The step-by-step solution leading up to this answer demonstrates the application of mathematical concepts such as percentages and fractions in a practical scenario. The process of calculating individual spending amounts and then comparing them showcases the importance of accurate arithmetic and problem-solving skills. This exercise not only answers the specific question but also reinforces the understanding of financial calculations and comparisons, which are valuable in everyday life. The final answer underscores the significance of each step in the solution, from understanding the problem to performing the calculations and drawing the final conclusion.

In conclusion, by carefully calculating the amounts Amina and Brody spent and then comparing them, we determined that Amina spends $£18$ more than Brody. This exercise demonstrates the practical application of basic mathematical concepts such as percentages and fractions in understanding real-world financial scenarios. The problem-solving process involved several key steps, including converting percentages to fractions, calculating a fraction of a whole, and finding the difference between two amounts. These skills are not only essential for academic purposes but also for making informed decisions in everyday life, such as managing personal finances and understanding economic data. The ability to accurately calculate and compare expenditures is a valuable asset in financial literacy. By breaking down the problem into smaller, manageable steps, we were able to arrive at a clear and concise solution. This approach highlights the importance of a systematic and logical methodology in problem-solving, which can be applied to a wide range of challenges beyond mathematics. The successful resolution of this problem reinforces the understanding of fundamental mathematical principles and their relevance in practical contexts.