Solving A Fabric Calculation Problem How Many Children's Costumes Were Sewn?
Hey guys! Let's dive into a cool math problem that involves calculating fabric usage in a sewing workshop, or as we call it, an atelier. This is a classic example of a word problem that helps us understand how math concepts apply to real-life situations. So, grab your thinking caps, and let's get started!
The Problem: Fabric, Dresses, and Costumes
Imagine you're running a bustling atelier, a place where beautiful garments are created. You start with a generous 150 meters of fabric. Now, the atelier receives an order to make 14 elegant women's dresses. Each of these dresses requires 3 meters of fabric. After completing the dresses, the remaining fabric is used to sew adorable children's costumes, each needing 2 meters of fabric. The big question we need to answer is: How many children's costumes were made in the atelier?
This problem is a fantastic way to practice our arithmetic skills, especially multiplication and subtraction, and then apply division to find the final answer. It's a step-by-step journey, so let's break it down together.
Step 1: Fabric for the Dresses
The first thing we need to figure out is how much fabric was used for the women's dresses. We know that 14 dresses were made, and each dress needed 3 meters of fabric. To find the total fabric used, we simply multiply the number of dresses by the fabric required per dress.
So, the calculation looks like this:
14 dresses * 3 meters/dress = 42 meters
This tells us that a total of 42 meters of fabric was used to create the 14 women's dresses. We've made a solid start, haven't we? Now, let's move on to the next step.
Step 2: Remaining Fabric
After making the dresses, there's some fabric left over. To figure out how much, we need to subtract the fabric used for the dresses from the total fabric we started with. Remember, we began with 150 meters, and we used 42 meters for the dresses.
Here's the subtraction:
150 meters (total) - 42 meters (dresses) = 108 meters
Great! We now know that there are 108 meters of fabric remaining. This is the fabric that will be used to make the children's costumes. We're getting closer to our final answer!
Step 3: Number of Children's Costumes
Now comes the exciting part – figuring out how many children's costumes can be made from the remaining fabric. We know that each costume requires 2 meters of fabric, and we have 108 meters of fabric available. To find the number of costumes, we need to divide the total remaining fabric by the fabric required per costume.
The division looks like this:
108 meters (remaining fabric) / 2 meters/costume = 54 costumes
Fantastic! We've found our answer! The atelier was able to make 54 children's costumes from the remaining fabric.
Conclusion: Problem Solved!
So, there you have it! By breaking down the problem into smaller, manageable steps, we were able to calculate the number of children's costumes made in the atelier. This problem demonstrates how basic math operations can be used to solve practical, real-world scenarios. Remember, the key to solving word problems is to read carefully, identify the important information, and then choose the correct operations to perform. Keep practicing, and you'll become a math whiz in no time!
Why This Problem Matters: Real-World Applications
This type of problem isn't just about numbers; it's about real-world applications of mathematics. Understanding how to calculate fabric usage, for example, is crucial in industries like fashion, textiles, and manufacturing. It helps businesses manage resources efficiently, minimize waste, and accurately estimate costs.
Imagine you're a fashion designer planning a new collection. You need to know how much fabric to order, how many garments you can produce, and how to price your items. The calculations we did in this problem are exactly the kind of calculations you'd use in that situation. It's about making informed decisions based on data, not just guesswork.
Moreover, this problem touches on the concept of resource allocation. The atelier had a limited amount of fabric and had to decide how to use it most effectively. This is a common challenge in many fields, from project management to finance. Understanding how to allocate resources efficiently is a valuable skill in both personal and professional life.
Tips for Tackling Similar Problems
Now that we've solved this problem, let's talk about some tips for tackling similar math problems in the future. Here are a few strategies that can help you become a problem-solving pro:
- Read Carefully and Understand the Question: The first step is always to read the problem carefully and make sure you understand what it's asking. What information is given? What are you trying to find?
- Identify Key Information: Once you understand the question, identify the key information you need to solve it. This might include numbers, measurements, and relationships between different quantities.
- Break the Problem into Smaller Steps: Complex problems can often be broken down into smaller, more manageable steps. This makes the problem less intimidating and easier to solve.
- Choose the Correct Operations: Decide which mathematical operations (addition, subtraction, multiplication, division) are needed to solve each step of the problem.
- Show Your Work: It's always a good idea to show your work, even if you can do some of the calculations in your head. This helps you keep track of your steps and makes it easier to find mistakes.
- Check Your Answer: Once you've found an answer, check it to make sure it makes sense in the context of the problem. Does it seem reasonable? Can you explain why your answer is correct?
Practice Makes Perfect
Like any skill, problem-solving gets easier with practice. The more you practice, the better you'll become at identifying patterns, choosing the right strategies, and solving problems efficiently. So, don't be afraid to tackle challenging problems. Each problem you solve is a step forward in your mathematical journey.
Let's Extend the Problem: What If...?!
To really solidify our understanding, let's think about some variations of this problem. This is a great way to challenge ourselves and explore different scenarios.
What if the atelier had a different amount of fabric?
Suppose the atelier had 200 meters of fabric instead of 150. How would this change the number of children's costumes they could make? We'd follow the same steps as before, but with a different starting amount. This helps us see how changing one variable affects the outcome.
What if the dresses required more fabric?
What if each women's dress required 3.5 meters of fabric instead of 3? This would mean less fabric would be available for the children's costumes. We'd calculate the new amount of fabric used for the dresses and then proceed as before.
What if the costumes required less fabric?
If each children's costume only needed 1.5 meters of fabric, the atelier could make more costumes with the remaining fabric. This helps us understand inverse relationships – when one quantity decreases, another might increase.
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