Calculating Shoe Cost A Step-by-Step Solution
In this article, we will delve into a mathematical problem involving Bridget's online shoe purchase. This is a great example of how math is used in everyday life. We'll break down the problem step-by-step to find the cost of each pair of shoes Bridget bought. To solve the question of how much each pair of shoes cost, we need to deconstruct the total bill and account for the shipping charges and sales tax. By carefully working backward through the calculations, we can isolate the cost of the shoes themselves and then divide by the number of pairs purchased. This exercise highlights the practical application of mathematical principles in managing personal finances and understanding the true cost of goods and services. Let's begin this mathematical journey together and uncover the price of those shoes!
Understanding the Problem
Before we dive into the solution, let's clearly understand the problem. Bridget purchased three pairs of shoes online, and the total bill amounted to $126.81. This total includes a shipping charge of $7.50 and a 6% sales tax on the total purchase price of the shoes. Our main objective is to determine the cost of each pair of shoes, assuming that all three pairs were priced the same. This problem involves several mathematical concepts, including percentages, addition, subtraction, and division. Understanding the initial conditions is crucial for setting up the correct equations and solving for the unknown variable, which in this case is the price of a single pair of shoes. By carefully identifying the given information and the desired outcome, we can create a roadmap for our solution and ensure that we arrive at the correct answer. So, let's proceed by outlining the steps we need to take to solve this problem and break it down into manageable parts.
Step 1: Subtract the Shipping Charge
The first step in solving this problem is to remove the shipping charge from the total bill. This will give us the subtotal before tax. The shipping charge is a fixed cost that does not depend on the price of the shoes, so we need to subtract it to isolate the amount that represents the cost of the shoes plus the sales tax. By subtracting the $7.50 shipping charge from the total bill of $126.81, we get: $126.81 - $7.50 = $119.31. This $119.31 represents the cost of the shoes plus the 6% sales tax. This step is crucial because it allows us to work with the amount that is directly related to the price of the shoes and the tax applied to them. Without removing the shipping charge, our subsequent calculations would be skewed, and we would not be able to accurately determine the cost of each pair of shoes. Now that we have this subtotal, we can move on to the next step, which involves accounting for the sales tax.
Step 2: Account for Sales Tax
Now that we have the subtotal before tax ($119.31), we need to account for the 6% sales tax. This means that $119.31 represents 106% of the original price of the shoes (100% for the original price plus 6% for the tax). To find the original price of the shoes before tax, we need to divide the subtotal by 1.06 (which represents 106% as a decimal). This calculation will undo the effect of the sales tax and give us the price of the shoes before tax was added. So, we divide $119.31 by 1.06: $119.31 / 1.06 = $112.56 (approximately). This $112.56 represents the total cost of the three pairs of shoes before tax. Understanding how to reverse the percentage calculation is essential for accurately determining the original price. Now that we have this value, we can proceed to the final step, which is to divide the total cost by the number of pairs of shoes to find the cost of each pair.
Step 3: Divide by the Number of Pairs
We've now determined that the total cost of the three pairs of shoes before tax was $112.56. To find the cost of each pair, we simply need to divide this total cost by the number of pairs, which is 3. So, we divide $112.56 by 3: $112.56 / 3 = $37.52. Therefore, each pair of shoes cost $37.52. This final step is straightforward but crucial for answering the original question. By dividing the total cost by the number of items, we arrive at the individual price, which is the ultimate goal of our problem-solving process. We have now successfully broken down the problem into manageable steps and arrived at the solution. Each pair of shoes cost $37.52, which is the answer to our question. This exercise demonstrates the power of mathematical reasoning in solving real-world problems.
Solution
After carefully working through the steps, we have arrived at the solution. Each pair of shoes that Bridget purchased cost $37.52. Let's recap the steps we took to reach this answer: 1. We subtracted the shipping charge ($7.50) from the total bill ($126.81) to get the subtotal before tax ($119.31). 2. We accounted for the 6% sales tax by dividing the subtotal ($119.31) by 1.06 to find the total cost of the shoes before tax ($112.56). 3. We divided the total cost of the shoes before tax ($112.56) by the number of pairs (3) to find the cost of each pair ($37.52). This step-by-step approach allowed us to break down the problem into smaller, more manageable parts, making it easier to solve. By understanding the relationships between the different components of the problem, such as the total bill, shipping charge, sales tax, and the number of pairs of shoes, we were able to systematically work towards the solution. This exercise highlights the importance of careful analysis and logical reasoning in solving mathematical problems.
Final Answer
Therefore, the final answer to the question, "How much did each pair of shoes cost?" is $37.52. This result was obtained by systematically working backward from the total bill, accounting for the shipping charge and sales tax, and then dividing the remaining cost by the number of pairs of shoes purchased. This detailed solution not only provides the answer but also demonstrates the process of problem-solving in a clear and understandable manner. By breaking down the problem into smaller steps, we were able to address each component individually and then combine the results to arrive at the final answer. This approach is applicable to a wide range of mathematical problems and can be a valuable tool for anyone looking to improve their problem-solving skills. We hope this explanation has been helpful and has provided a clear understanding of how to solve this type of problem.
Conclusion
In conclusion, this problem illustrates how mathematical principles can be applied to solve real-world scenarios. By carefully analyzing the given information and breaking down the problem into smaller, manageable steps, we were able to determine the cost of each pair of shoes that Bridget purchased. This exercise highlights the importance of understanding percentages, subtraction, division, and logical reasoning in everyday life. The ability to solve problems like this is not only valuable in academic settings but also in personal finance and decision-making. We hope this article has provided a clear and comprehensive explanation of the solution and has encouraged you to think critically about how math is used in the world around us. Whether it's calculating the cost of goods, managing a budget, or understanding financial statements, mathematical skills are essential for navigating the complexities of modern life.
