Notebook Cost With Discount: A Math Problem Solved
Hey guys! Let's dive into this math problem about a merchant buying notebooks and getting a sweet anniversary deal. We'll break it down step-by-step so it's super clear. Get ready to sharpen your pencils (or, you know, your minds!).
Understanding the Problem
In this mathematical scenario, we've got a merchant who's planning to stock up on notebooks. Each notebook has a price tag of S/. 4.5. However, there's a twist! It's the store's anniversary, and they're offering a special deal: for every dozen notebooks purchased, the merchant gets one notebook absolutely free. Our main goal here is to figure out exactly how much the merchant ended up paying if they walked away with a grand total of 260 notebooks. We've got a few options to choose from: A) S/. 900, B) S/. 1000, C) S/. 1080, and D) S/. 1200. So, how do we crack this? Let's get into the nitty-gritty of solving this problem.
Breaking Down the Discount
The key here is the anniversary discount – one free notebook for every dozen purchased. This means for every 12 notebooks the merchant pays for, they actually receive 13. This changes the way we think about the price per notebook because effectively, the cost per notebook decreases due to the free ones. To tackle this, we need to figure out how many sets of 13 notebooks (12 paid + 1 free) are included in the 260 notebooks the merchant received. This involves division and understanding how the discount impacts the overall cost. We're not just calculating the price for 260 notebooks at the original rate; we're calculating it considering this beneficial discount. This is where the real math magic happens, and we start to see how the free notebooks influence the final amount paid. So, let's keep this discount in mind as we move forward – it's the core of the solution.
Calculating the Number of Dozens and Free Notebooks
Okay, so we know the merchant ended up with 260 notebooks, and for every dozen they bought, they snagged an extra one for free. This means they got 13 notebooks for the price of 12. To figure out how many sets of 13 notebooks are in 260, we need to do some division. 260 divided by 13 gives us the number of dozens the merchant effectively purchased. This calculation will tell us how many times the "buy 12, get 1 free" deal was applied. Once we know this, we can then figure out exactly how many notebooks the merchant paid for. This is a crucial step because it directly impacts the total cost. We're essentially reversing the discount to find out the original number of notebooks that were paid for before the freebies were added. It's like detective work, but with numbers! This step gets us closer to the final answer by pinpointing the actual quantity of notebooks that contributed to the total bill.
Determining the Total Cost
Now that we know how many notebooks the merchant actually paid for, we can calculate the total cost. Remember, each notebook has a price of S/. 4.5. So, to find the total amount spent, we simply multiply the number of notebooks paid for by the price per notebook. This is straightforward multiplication, but it's a critical step in solving the problem. It directly translates the quantity of notebooks into a monetary value. This calculation will give us the final answer, the amount the merchant shelled out for their notebook haul. We're taking the discounted number of notebooks and applying the individual price to arrive at the total cost. It's like the grand finale of our math problem, bringing all the pieces together to reveal the solution. So, let's crunch those numbers and see what the final bill comes to!
Solving the Problem Step-by-Step
Alright, let's put on our math hats and work through this problem together, step by step, so everything is crystal clear.
Step 1: Find the Number of Sets of 13 Notebooks
Remember, the merchant received 260 notebooks in total, and they got one free for every dozen purchased, meaning they received 13 notebooks for every 12 they paid for. So, the first thing we need to do is figure out how many sets of 13 notebooks are in 260. We can do this by dividing the total number of notebooks (260) by 13:
260 notebooks / 13 notebooks per set = 20 sets
This tells us that the merchant effectively purchased 20 sets of 12 notebooks to get 20 free notebooks, resulting in a total of 260 notebooks. This is a crucial step because it helps us understand how the discount impacted the purchase. We're not just looking at 260 individual notebooks; we're looking at groups of 13, which includes the freebies. Understanding these sets is key to calculating the actual cost. It's like breaking down a big problem into smaller, more manageable chunks. So, we now know the merchant bought 20 "deals" where they got 13 notebooks each time. Let's move on to the next step and see how this affects the final price.
Step 2: Calculate the Number of Notebooks Paid For
Now that we know the merchant bought 20 sets of notebooks (where each set consists of 12 paid notebooks and 1 free), we can figure out the total number of notebooks they actually paid for. To do this, we simply multiply the number of sets (20) by the number of notebooks paid for in each set (12):
20 sets * 12 notebooks per set = 240 notebooks
So, the merchant paid for 240 notebooks in total. This is a pivotal number because it's the basis for calculating the final cost. We've successfully isolated the number of notebooks that contributed to the bill, excluding the free ones. This step clarifies the exact quantity of notebooks that were purchased at the original price. It's like peeling back the layers of the discount to reveal the core number of items bought. With this information, we're one step closer to the grand total. We've transformed the problem from dealing with 260 notebooks to focusing on the 240 notebooks that were actually paid for. Let's see how this plays out in the next step.
Step 3: Calculate the Total Amount Paid
We've arrived at the final calculation! We know the merchant paid for 240 notebooks, and each notebook costs S/. 4.5. To find the total amount paid, we multiply the number of notebooks by the price per notebook:
240 notebooks * S/. 4.5 per notebook = S/. 1080
Therefore, the merchant paid S/. 1080 for the notebooks. Woohoo! We've cracked the code and found our answer. This calculation is the culmination of all our previous steps, bringing together the number of notebooks paid for and the individual price to arrive at the total cost. It's the final piece of the puzzle, solidifying our solution. This result shows the actual monetary value of the purchase, taking into account the fantastic anniversary discount. So, after all the calculations, the merchant's bill came to S/. 1080. We've successfully navigated the problem and found the correct answer.
The Answer
So, after carefully working through the problem, we've determined that the merchant paid a total of S/. 1080 for the notebooks. Looking back at our options:
A) S/. 900 B) S/. 1000 C) S/. 1080 D) S/. 1200
The correct answer is C) S/. 1080. We nailed it! This whole process has shown how breaking down a problem into smaller steps can make it much easier to solve. We started by understanding the discount, then calculated the number of sets, figured out how many notebooks were paid for, and finally, computed the total cost. Each step built upon the previous one, leading us to the right answer. It's a great feeling when all the pieces come together, isn't it? So, give yourself a pat on the back for following along and understanding this problem. Math can be fun when we tackle it together!
Key Takeaways
Okay, guys, let's recap the key takeaways from this notebook-buying adventure. First and foremost, understanding the discount is crucial. We had to really grasp the "buy a dozen, get one free" deal to solve this effectively. This meant not just looking at the total number of notebooks but also how they were bundled due to the promotion. This is a common theme in real-world math problems – discounts and special offers can change the way we calculate costs. So, always pay close attention to those deals! They can significantly impact the final price, as we saw here. Ignoring the discount would have led us to the wrong answer, highlighting the importance of reading the problem carefully and identifying all the relevant details.
Secondly, breaking the problem down into smaller steps made it much less daunting. We didn't try to tackle everything at once. Instead, we focused on calculating the number of sets of notebooks, then the number paid for, and finally the total cost. This step-by-step approach is a powerful strategy for tackling complex problems, not just in math but in life! It allows us to manage the information more effectively and avoid getting overwhelmed. Each step acts as a mini-goal, making the overall problem seem more achievable. So, remember to break things down – it's a game-changer!
Lastly, accurate calculations are non-negotiable. A small error in any step could have thrown off the final answer. Whether it was dividing, multiplying, or subtracting, we needed to be precise. This underscores the importance of checking our work and being meticulous in our approach. Math is a precise language, and even a tiny slip can lead to a completely different result. So, always double-check your calculations and ensure you're using the correct operations. Precision is your friend in the world of math, and it's what ultimately leads us to the correct solution. So, keep those calculations sharp and accurate!
Practice Problems
Alright, guys, let's keep those math muscles flexed! Here are a couple of practice problems to help you solidify your understanding of this concept. Remember the steps we used – break down the problem, identify the discount (if any), and calculate carefully. You've got this!
- A store is selling pens for S/. 2 each. For every 10 pens purchased, customers get an extra pen for free. If a customer wants to buy 132 pens, how much will they pay?
- A bakery sells cookies for S/. 3.5 each. They have a special offer: buy a half-dozen and get one cookie free. If someone buys 84 cookies, how much will they spend?
Try tackling these problems on your own, using the strategies we discussed. Don't be afraid to revisit the steps and examples we've covered in this article. Practice makes perfect, and the more you work through these types of problems, the more confident you'll become. These problems are designed to test your understanding of discounts, bundling, and overall cost calculation. They're similar to the notebook problem we solved, but with different scenarios and numbers. This variety helps reinforce the core concepts and allows you to apply them in different contexts. So, grab a pencil, a piece of paper, and get those problem-solving skills in action! You'll be amazed at how much you can achieve with a little practice and perseverance.
Conclusion
So, there you have it! We've successfully navigated the notebook-buying problem, learned about discounts, and sharpened our math skills. Remember, the key is to break down the problem, understand the conditions (like the anniversary discount), and calculate carefully. With these tools in your arsenal, you'll be able to tackle similar problems with confidence. Math isn't just about numbers; it's about problem-solving and critical thinking, skills that are valuable in all aspects of life. This journey through notebooks and discounts has highlighted the importance of paying attention to details, using a step-by-step approach, and ensuring accuracy in our calculations. These are lessons that extend far beyond the realm of mathematics. So, keep practicing, keep exploring, and most importantly, keep enjoying the process of learning. Math can be a fascinating and rewarding subject when approached with the right mindset and strategies. So, go forth and conquer those math challenges!
