Soda Stock: A Step-by-Step Math Solution
Hey everyone! Let's tackle a fun math problem involving sodas in a warehouse. This is a classic example of a word problem where we need to break it down step by step to find the solution. So, grab your thinking caps, and let's dive in!
Understanding the Initial Stock
First things first, we need to figure out how many sodas we actually start with. The problem mentions "siete docenas y media," which translates to seven and a half dozens. Now, a dozen is 12, so we have 7.5 multiplied by 12. Let's break this down:
- Seven dozens: 7 * 12 = 84 sodas
- Half a dozen: 0.5 * 12 = 6 sodas
Adding these together, 84 + 6, gives us a total of 90 sodas initially in the warehouse. So, we're starting with a pretty well-stocked bodega! Knowing the initial amount is crucial for solving the rest of the problem. Without this first step, we'd be lost in a sea of fractions and calculations. Remember, guys, always start by understanding the basics before moving on to more complex operations. A solid foundation is key to problem-solving success. This initial calculation sets the stage for everything else we'll do, so make sure you've got it down. We've established that we're starting with 90 bottles of soda, and now we can move on to the next part of the problem: the sales.
Calculating the Sales
Okay, now we know we have 90 sodas. The problem states that 2/3 of the total sodas are sold. So, how many sodas is that exactly? To figure this out, we need to calculate 2/3 of 90. Here's how we do it:
- (2/3) * 90 = (2 * 90) / 3 = 180 / 3 = 60 sodas
So, 60 sodas were sold. That's a pretty good day for soda sales! It's important to understand what this number represents in the context of the problem. We're not just calculating a fraction; we're figuring out how many sodas left the warehouse. This step helps us move closer to the final answer, which is the number of sodas remaining. Now that we know how many sodas were sold, we can figure out how many sodas are left before the new purchase. This is a crucial step because the next part of the problem involves adding sodas back into the inventory. Think of it like this: we started with a full warehouse, sold some sodas, and now we need to figure out how much space we have left before we restock. Understanding this flow of goods in and out of the warehouse is key to solving the problem correctly. This calculation is also a good example of how fractions are used in real-world scenarios, like managing inventory or calculating discounts. So, mastering this skill is not just about solving math problems; it's about developing practical skills that can be applied in many different situations.
Determining Remaining Stock After Sales
Alright, we know we started with 90 sodas and sold 60. To find out how many sodas are left, we simply subtract the number of sodas sold from the initial number:
- 90 (initial) - 60 (sold) = 30 sodas
So, after selling 2/3 of the sodas, there are 30 sodas remaining in the warehouse. This is an important intermediate result. We need this number to calculate the next part of the problem, which involves buying more sodas. Think of it like a checkpoint in our calculation journey. We've cleared one hurdle and now we're ready to move on to the next. It's also worth noting that this type of calculation – subtracting what's taken away from the total – is a fundamental skill in math and everyday life. Whether you're managing your budget, tracking your expenses, or just figuring out how much pizza is left, the ability to subtract is crucial. So, remember this step: find the difference between the initial amount and what's been used or sold. This will help you solve many different problems, not just soda-related ones. And always double-check your work, guys! A simple mistake in subtraction can throw off the entire calculation.
Calculating the New Purchase
Now, the problem says that 1/3 of the remaining sodas are purchased. We know there are 30 sodas remaining, so we need to find 1/3 of 30. Here's how we do it:
- (1/3) * 30 = 30 / 3 = 10 sodas
So, 10 more sodas are bought and added to the warehouse. It's crucial to understand that this purchase is based on the number of sodas remaining after the initial sales, not the original amount. This is a common trick in word problems – they often include information that needs to be processed in a specific order. If we had calculated 1/3 of the original 90 sodas, we would have gotten the wrong answer. This step highlights the importance of careful reading and understanding the sequence of events described in the problem. We're not just dealing with numbers here; we're dealing with a real-world scenario of buying and selling goods. Visualizing this process can help us avoid making mistakes and ensure that we're performing the correct calculations at each step. So, always remember to consider the context of the problem and the order in which things happen. This will make you a much better problem solver, both in math and in life.
Determining the Final Stock
Finally, to find out how many sodas are in the warehouse now, we need to add the newly purchased sodas to the remaining stock:
- 30 (remaining) + 10 (purchased) = 40 sodas
Therefore, there are now 40 bottles of soda in the warehouse. We've reached the end of our calculation journey! This is the final answer to the problem. We started with an initial stock, calculated the sales, determined the remaining stock, calculated a new purchase, and finally, arrived at the final count. Each step was dependent on the previous one, highlighting the importance of careful and methodical problem-solving. It's also a good idea to take a moment and reflect on the entire process. Did our answer make sense in the context of the problem? We started with 90 sodas, sold a majority of them, and then added a smaller number back in. So, ending up with 40 sodas seems reasonable. This type of logical thinking is crucial for verifying your answers and ensuring that you haven't made any major errors along the way. So, always take that extra moment to double-check and think through your solutions.
Conclusion
So, there you have it! By breaking down the problem into smaller, manageable steps, we were able to find the solution. Remember, guys, math problems are like puzzles – each piece needs to fit in the right place to get the complete picture. Keep practicing, and you'll become master problem-solvers in no time!
