Solving The Fabric Store Problem: A Step-by-Step Guide

by TextBrain Team 55 views

Hey there, fellow math enthusiasts! Let's dive into a classic word problem that combines a bit of algebra with everyday scenarios. This problem involves a fabric store and the quantities of different types of fabrics it sold. Don't worry, it's not as intimidating as it sounds! We'll break it down step by step, ensuring you grasp the concepts and can tackle similar problems with confidence. So, grab a cup of coffee, and let's get started! This problem is a great example of how math can be used to solve practical, real-world situations. We'll use basic arithmetic and logical reasoning to find the solution. You'll see that with a little bit of patience and the right approach, even seemingly complex problems can be easily solved. This kind of problem helps build a strong foundation in understanding ratios, proportions, and problem-solving strategies, skills that are valuable in many areas of life, not just academics. The ability to break down a problem into smaller, manageable parts is a crucial skill. It's what makes complex tasks less daunting and more achievable. This approach not only helps in solving the problem at hand but also in developing critical thinking skills that are applicable in various aspects of life. Therefore, let's work through this problem together. We'll explore each component thoroughly, ensuring you're equipped with the knowledge and methods to solve it. This is a great way to sharpen your math skills and enjoy the process of problem-solving! The key here is to carefully read the problem, understand the given information, and use logical steps to find the solution.

Understanding the Problem

Let's start by understanding the problem. A fabric store sold several types of fabric, including cotton, satin, and silk. We are given the following information:

  • The store sold 4620 meters of cotton.
  • The store sold satin in an amount 3 times less than cotton.
  • The store sold silk in an amount 4 times less than cotton.

The goal is to determine the total amount of fabric the store sold. This is a straightforward arithmetic problem that requires us to compute the amounts of satin and silk sold and then add all three quantities together. The problem provides all the necessary information to find the solution. It is presented in a clear and concise manner, which helps us focus on the core task: applying the right steps to calculate the answer. Always pay attention to the details, as they are essential for getting the right solution. In essence, each piece of information is a clue that leads us closer to the solution. Let's break down the problem further. The first step is to identify the known and unknown quantities. We know how much cotton the store sold, but we need to find out how much satin and silk were sold. Understanding these specifics helps in planning the solution. Then, we will use the given relationships to calculate the quantities of satin and silk. This will involve either division. Once we have calculated the amounts of satin and silk, we can simply add all the quantities together to get the total amount of fabric sold. Breaking down the problem into simpler steps is the easiest approach.

Calculating the Amount of Satin and Silk

Now, let's calculate the amounts of satin and silk. The problem states that the store sold satin in an amount 3 times less than cotton. Since the store sold 4620 meters of cotton, we need to divide the amount of cotton by 3 to find the amount of satin.

  • Amount of Satin = Amount of Cotton / 3
  • Amount of Satin = 4620 meters / 3 = 1540 meters

Next, we need to calculate the amount of silk. The problem states that the store sold silk in an amount 4 times less than cotton. To find the amount of silk, we divide the amount of cotton by 4.

  • Amount of Silk = Amount of Cotton / 4
  • Amount of Silk = 4620 meters / 4 = 1155 meters

So, the store sold 1540 meters of satin and 1155 meters of silk. These calculations are fundamental. They show how the relationships between the different fabric types are used to find the quantities of each. This approach demonstrates how understanding the ratios can lead to accurate calculations. To ensure that we get the right answer, we need to divide the cotton amount by the correct number. Make sure you read the information in the question accurately. In this case, the question specifies that the store sold satin in an amount 3 times less than cotton, meaning we divide by 3. Likewise, it states that silk was sold in an amount 4 times less than cotton, so we divide by 4. Always double-check your work to avoid calculation mistakes.

Finding the Total Amount of Fabric

Finally, let's calculate the total amount of fabric the store sold. We know:

  • Amount of Cotton = 4620 meters
  • Amount of Satin = 1540 meters
  • Amount of Silk = 1155 meters

To find the total amount, we simply add these three amounts together:

  • Total Amount = Amount of Cotton + Amount of Satin + Amount of Silk
  • Total Amount = 4620 meters + 1540 meters + 1155 meters = 7315 meters

Therefore, the store sold a total of 7315 meters of fabric. This final step involves summing up all the individual quantities we've calculated to find the total amount. It shows how all the components are put together to get the final answer. This is an effective way to organize and finalize the solution to the problem. Once the individual quantities are found, adding them together becomes an easy task. Remember that accuracy is essential. Verify that all of your calculations are correct and that no information is missed. The last step in this problem is a testament to the effectiveness of dividing a complex problem into smaller, more manageable parts.

Conclusion

And there you have it! We successfully solved the problem. The fabric store sold a total of 7315 meters of fabric. This exercise illustrates how to break down word problems into easy-to-manage components. By carefully reading the problem, extracting the necessary information, and using the appropriate mathematical operations, we arrived at the solution. Remember, practice is key to improving your problem-solving skills. The more problems you solve, the more comfortable and confident you will become in your abilities. Also, use this method to tackle other word problems. The methodical approach used here can be applied to a variety of similar scenarios. Always make sure you're careful when reading the information in the question. This helps ensure you extract all the right information, so you can get the right answer. And most importantly, don't hesitate to ask for help or clarification if you're stuck. Math is a skill that everyone can learn and improve. With the right methods and practice, you can become a pro. Keep up the great work, and keep exploring the fascinating world of mathematics!