Party Favor Frenzy: Lonni's Bag Bonanza!
Hey everyone, let's dive into a fun math problem! We're going to help Lonni figure out just how many awesome party favors he snagged. Get ready to put on your thinking caps, because it's time to crunch some numbers! The original problem states there are 5 party favors in each bag, and Lonni buys 7 bags, then he buys 3 more bags. How many favors did Lonni buy? Let's break it down step by step to make it super easy to understand. We'll explore different approaches to solving this problem, ensuring we understand the concepts involved and can apply them to similar scenarios. This isn't just about finding an answer; it's about developing strong problem-solving skills that you can use in all aspects of life, from managing your allowance to planning a party of your own!
Understanding the Problem
Understanding the problem is key, right? First off, let's make sure we're all on the same page. We have a situation involving party favors, which, let's be honest, are a staple of any good party! Lonni is the main character in our math story today, and he's on a mission to collect as many favors as possible. The problem tells us that each bag of favors contains exactly 5 items. Think of it like a treasure chest with a set number of goodies inside. Lonni initially buys a certain number of these bags, which is where our first calculation begins. Then, like any good party planner, he realizes he needs even more, so he goes back and grabs some extra bags. This is where the plot thickens! The question we need to answer is: How many total favors does Lonni end up with? We're not just looking for a simple yes or no answer; we want to know the grand total of all the favors Lonni acquired. This involves figuring out the initial amount, adding the extra amount, and arriving at our final answer. It's like collecting puzzle pieces; we need to find the number in the first purchase, the number in the second purchase, and then put them all together to complete the picture. So, Lonni's Party Favor Quest boils down to simple multiplication and addition – two fundamental operations in mathematics. This is not just a math problem, it's a real-life scenario that showcases how math helps us solve everyday challenges. So, let's arm ourselves with the knowledge and tools needed to crack this problem and see how many party favors Lonni managed to collect. Don't worry, it's going to be a fun journey through the world of numbers!
Breaking Down the Math
Let's get down to the nitty-gritty and break down the math. The initial scenario involves Lonni buying 7 bags, and each bag contains 5 favors. To find out how many favors are in these 7 bags, we need to multiply the number of bags by the number of favors per bag. This is basic multiplication: 7 bags * 5 favors/bag = 35 favors. So, just from the first purchase, Lonni has already accumulated 35 party favors. Not bad, Lonni! But the adventure doesn't stop there. He then decides to buy 3 more bags. Each of these bags also contains 5 favors. We repeat the same multiplication process: 3 bags * 5 favors/bag = 15 favors. Therefore, Lonni gets an additional 15 favors from his second purchase. Now, to find out the total number of favors Lonni has, we need to add the favors from his first purchase to the favors from his second purchase. We simply add 35 favors + 15 favors = 50 favors. That is a lot of party favors. So, with a little multiplication and addition, we have successfully figured out the total number of favors Lonni acquired. It is as easy as that. This simple problem beautifully illustrates how basic math skills can be applied to solve real-world situations. Each step brings us closer to the correct answer, and it all builds on the foundation of understanding the question, choosing the right operation, and performing the calculation accurately. Keep practicing these skills, and you'll become a math whiz in no time!
Solving Step-by-Step
Okay, guys, let's walk through this step-by-step to make sure we're crystal clear on the process. First, let's identify the information we have. We know that each bag has 5 favors, Lonni initially buys 7 bags, and then he grabs 3 more bags. Our goal is to calculate the total number of favors. The first step is to calculate the number of favors from the first purchase. We multiply the number of bags (7) by the number of favors per bag (5). 7 * 5 = 35 favors. So Lonni has 35 favors from his initial shopping spree. Next up, let's find out how many favors are in the additional 3 bags. We multiply 3 bags by 5 favors per bag: 3 * 5 = 15 favors. Finally, to find the total, we add the favors from the first purchase (35) to the favors from the second purchase (15). 35 + 15 = 50 favors. So, the final answer is 50 favors. We started with the basic information, performed two simple multiplication calculations, and then added the results together to find the grand total. Each step is important. By following this method, we broke down a slightly more complex problem into smaller, easier-to-manage steps, making it much less daunting. This problem-solving approach isn't just limited to math; it's a great strategy for tackling any challenge. Breaking down a complex task into smaller steps, understanding each step, and then combining the steps to find a solution is the key to success. This method helps prevent mistakes and ensures that you can understand the process and the answer. Remember to review your work and make sure that it all adds up! Math problems are best tackled when you approach them with organization and a clear plan.
Calculation Breakdown
Alright, let's break down the calculations in more detail. We've already touched on the core steps, but let's make sure we understand the 'why' behind each one. In the first part of the problem, we need to find the total favors in the initial 7 bags. This requires multiplication because we're repeatedly adding the same number (5 favors) seven times. So, the calculation is 7 (bags) * 5 (favors/bag) = 35 favors. This tells us how many favors Lonni had after his first trip to the store. Then, Lonni goes back for more. He buys 3 additional bags, each with 5 favors. To find the total favors in these bags, we perform the same multiplication: 3 (bags) * 5 (favors/bag) = 15 favors. This tells us the quantity of additional favors. In the final step, we combine these two totals. We add the 35 favors from the first purchase and the 15 favors from the second purchase to get the grand total. 35 + 15 = 50 favors. This addition step combines all the favors Lonni acquired. It is really that simple. Through multiplication and addition, we've solved the problem. Each calculation has a clear purpose. This breakdown of the calculations shows how we move from the original information to the final answer. Understanding each step helps solidify your understanding of how to approach these kinds of problems, and the ability to break them down into smaller steps is important.
The Correct Answer and Explanation
So, after all that work, what's the correct answer and explanation? The correct answer is (B) 50. Lonni bought a total of 50 party favors. To recap, Lonni bought 7 bags initially, and each bag contained 5 favors. Then, he bought 3 more bags, each also containing 5 favors. So, we first found the total favors in the first purchase: 7 bags * 5 favors/bag = 35 favors. Next, we found the total favors in the second purchase: 3 bags * 5 favors/bag = 15 favors. Finally, we added the favors from both purchases: 35 favors + 15 favors = 50 favors. Therefore, Lonni ended up with 50 favors. The other options, (A) 35 and (C) 15, are incorrect because they don't represent the total number of favors when taking both purchases into account. Option (A) 35 only represents the number of favors from the first purchase, and option (C) 15 represents only the number of favors from the second purchase. The key to answering the question correctly is to perform all the necessary calculations and to ensure that you are considering every part of the problem. This problem is a prime example of a multi-step math problem that can be easily solved when broken down into manageable steps. Remember to always go back and check your work to ensure that you haven't overlooked any details!
Why Option (B) is Correct
Let's zero in on why option (B) is correct. Option (B) states that Lonni bought 50 party favors. We got this answer by following all the steps in our previous explanations. First, we calculated the total favors in the first 7 bags: 7 bags * 5 favors/bag = 35 favors. Next, we calculated the favors in the additional 3 bags: 3 bags * 5 favors/bag = 15 favors. Finally, we added the favors from both purchases: 35 favors + 15 favors = 50 favors. This final calculation gives us the total number of party favors Lonni purchased. Other options are incorrect because they do not reflect the complete calculation needed to solve the problem. Option (A), 35, only takes into account the first set of bags. It is a good first step, but not the final answer. Option (C), 15, is even further from the final answer because it only shows the number of favors in the additional bags. Option (B), 50, combines all the information in the problem. By correctly applying the multiplication and addition, we get the correct final answer, demonstrating the power of understanding how to break a problem into smaller parts and solving them logically. This step-by-step approach not only ensures accuracy but also reinforces the underlying math concepts.
Tips for Similar Problems
Alright, guys, let's talk about some tips for similar problems. You will definitely encounter similar word problems in the future. Here's a few things to keep in mind. First, always read the problem carefully. Understand exactly what the question is asking. Sometimes, the language can be a little tricky, so take your time to break down each sentence. Second, identify the key information. Highlight the numbers and the crucial details. For example, in this problem, we need to know the number of favors per bag and the number of bags Lonni bought. Third, choose the right operation. In this case, we used multiplication and addition. Recognize when to use multiplication (when dealing with groups of items) and when to use addition (when combining quantities). Fourth, break down the problem into smaller steps. Make the problem less overwhelming by tackling it one step at a time. This keeps you focused and prevents errors. Fifth, write out the steps. This helps you track your work and makes it easier to find any mistakes. Sixth, check your answer. Always go back and reread the problem and check your calculations. Make sure your answer makes sense in the context of the problem. Finally, practice, practice, practice! The more you solve these types of problems, the easier they become. Look for similar problems in your textbook or online and work through them, applying these strategies. If you follow these tips, you'll find that solving word problems becomes a whole lot easier! Good luck and happy solving!