Ordering Items By Price From Most Expensive To Least Expensive
In this article, we'll tackle a practical problem involving percentage changes and ordering items based on their final prices. Our goal is to arrange a given set of items – a blender and a hat – from the most expensive to the least expensive after considering the price changes. This exercise combines basic arithmetic with an understanding of percentages, a crucial skill in everyday financial calculations. We will delve into the mathematics behind calculating price changes, understanding the impact of percentage increases on the original prices. By carefully analyzing the base prices and the percentage changes, we can accurately determine the final prices of the items and arrange them in the desired order. This task not only sharpens our mathematical abilities but also provides valuable insights into real-world scenarios where price fluctuations play a significant role in purchasing decisions.
Understanding the Problem
To begin, let's clearly define the problem. We are presented with a list of items, each having a base price and a percentage change. The percentage change indicates the amount by which the base price has increased. Our objective is to calculate the final price of each item after applying the percentage change and then arrange the items in descending order of their final prices, from the most expensive to the least expensive. This involves a two-step process: first, calculating the price increase for each item, and second, adding the increase to the base price to determine the final price. For instance, if an item has a base price of $100 and a 10% increase, we need to calculate 10% of $100, which is $10, and then add it to the base price, resulting in a final price of $110. We'll apply this method to each item in our list, ensuring we understand the magnitude of the percentage change and its effect on the initial cost. Once we have the final prices, we can easily compare them and arrange the items accordingly, gaining a clear understanding of their relative values after the price adjustments.
Calculating the Final Price
Now, let's dive into the calculations. To determine the final price of an item after a percentage increase, we use the following formula:
Final Price = Base Price + (Base Price * Percentage Change)
Where the percentage change is expressed as a decimal. For example, a 9% increase would be represented as 0.09. Let's apply this formula to the blender. The blender has a base price of $29.73 and a 9% increase. First, we calculate the price increase:
Price Increase (Blender) = $29.73 * 0.09 = $2.6757
Then, we add this increase to the base price to get the final price:
Final Price (Blender) = $29.73 + $2.6757 = $32.4057
Rounding to two decimal places, the final price of the blender is approximately $32.41. Now, let's repeat this process for the hat. The hat has a base price of $14.16 and a 77% increase. We calculate the price increase:
Price Increase (Hat) = $14.16 * 0.77 = $10.9032
Then, we add this increase to the base price to get the final price:
Final Price (Hat) = $14.16 + $10.9032 = $25.0632
Rounding to two decimal places, the final price of the hat is approximately $25.06. By systematically applying this formula to each item, we can accurately determine their final prices after accounting for the percentage changes and their respective impacts, ensuring a solid foundation for comparison and ordering.
Comparing the Final Prices
With the final prices calculated, we can now compare the prices of the blender and the hat. We found that the blender has a final price of approximately $32.41, while the hat has a final price of approximately $25.06. By directly comparing these two amounts, it becomes clear that the blender is more expensive than the hat after the price changes. This simple comparison highlights the importance of calculating final prices when dealing with percentage increases, as the item with the higher base price may not always be the more expensive one after the increase is applied. In this case, even though the hat had a substantial percentage increase (77%), the blender's lower percentage increase (9%) on a higher base price resulted in a higher final price. This emphasizes the interplay between base price and percentage change in determining the ultimate cost of an item. Understanding this relationship is essential for making informed purchasing decisions and accurately comparing the values of different items.
Ordering the Items
Now that we have compared the final prices, we can confidently order the items from the most expensive to the least expensive. Based on our calculations, the blender has a final price of $32.41, and the hat has a final price of $25.06. Therefore, the order from most expensive to least expensive is:
- Blender ($32.41)
- Hat ($25.06)
This ordering process demonstrates how mathematical calculations can be applied to real-world scenarios, such as comparing prices and making informed purchasing decisions. By carefully calculating the final prices after percentage changes, we can accurately rank the items based on their cost. This ability to apply mathematical concepts to practical situations is a valuable skill that can help us navigate various financial and decision-making contexts. The methodical approach we used – calculating individual price changes, determining final prices, and then comparing those prices – ensures a clear and accurate ordering of items based on their cost.
Conclusion
In conclusion, we have successfully ordered the items – a blender and a hat – from the most expensive to the least expensive by carefully considering their base prices and percentage changes. We applied a simple yet effective formula to calculate the final price of each item after the price increase, and then we compared these final prices to determine the correct order. This exercise demonstrates the practical application of basic mathematical concepts, particularly percentages, in everyday financial situations. Understanding how to calculate percentage changes and their impact on prices is crucial for making informed purchasing decisions and effectively managing personal finances. This problem-solving approach not only enhances our mathematical skills but also empowers us to analyze and interpret price information accurately. By mastering these concepts, we can confidently navigate real-world scenarios where price fluctuations play a significant role, ensuring we make well-informed choices and get the best value for our money.
