School Seating: Can 50 Students Fit?

Hey guys, let's dive into a fun math problem! We've got a school with a specific seating arrangement, and we need to figure out if it can handle a certain number of students. It's like a real-world puzzle, and it's super practical. So, the scenario is this: there are five four-person benches, two three-person benches, and four benches that can seat either four or five people. The big question: can this school accommodate 50 students? Let’s break it down step by step to find out. This kind of problem isn't just about numbers; it's about understanding how to solve practical issues with a little bit of math smarts. We're going to calculate the maximum capacity of each type of bench and then add them all up to see if it can hold 50 students. Ready to crack the code?

Calculating Bench Capacity

Alright, first things first, let's figure out how many students each type of bench can hold. This is the foundation of our calculation, so pay close attention. We will start with the easiest part: the four-person benches. We have five of these, and each can hold four students. To find the total capacity of these benches, we multiply the number of benches by the capacity of each bench: 5 benches * 4 students/bench = 20 students. So far, the four-person benches can hold 20 students. Next, we consider the three-person benches. There are two of these, and each holds three students. The calculation is pretty straightforward: 2 benches * 3 students/bench = 6 students. Easy peasy! These benches can accommodate 6 students. Now comes the trickier part: the benches that can seat either four or five students. There are four of these. To get the maximum capacity, we assume each of these benches can hold five students (since the question is whether the school can fit 50 students). So, 4 benches * 5 students/bench = 20 students. Adding this to the previous calculations, the school's benches have a total capacity of 20 + 6 + 20 = 46 students. This step is crucial, because it sets the stage for the final comparison. Remember, understanding each part of the problem is key to solving it correctly. We carefully calculated the capacity for each type of bench to make sure we got the right answer!

Total Capacity and Comparison

Now that we've figured out how many students each type of bench can hold, it's time to add everything up to find the total capacity of the school's seating. We know that the four-person benches can hold 20 students, the three-person benches can hold 6 students, and the benches that seat four or five can hold a maximum of 20 students. To find the total, we add these numbers together: 20 students + 6 students + 20 students = 46 students. So, the total seating capacity of the school is 46 students. This is a super important number because it gives us the limit, the maximum number of students the school can possibly fit. We now compare this total capacity with the number of students we want to accommodate, which is 50. We've got a capacity of 46, and we need to fit 50 students. It's pretty simple: 46 is less than 50. This means the school's seating capacity is not enough to accommodate 50 students. Think of it like this: the seats are the container, and the students are what we're trying to fit in. The container just isn't big enough! So, to answer the original question: no, the school cannot accommodate 50 students with its current seating arrangement.

Final Thoughts

So, guys, we've successfully solved the problem! We started with the question of whether a school with a specific bench arrangement could fit 50 students. By calculating the capacity of each type of bench and adding them up, we determined that the school's maximum seating capacity is 46 students. Comparing this to the target number of 50 students, we concluded that the school cannot accommodate all the students with the current seating arrangement. This exercise shows how important it is to break down complex problems into smaller, manageable steps. We carefully calculated the capacity of each type of bench, added them up, and made a simple comparison. The skills we used here, like understanding multiplication and addition, are fundamental in everyday problem-solving. This problem also highlights the importance of paying attention to detail and ensuring that we're using the correct information for each calculation. Whether you're figuring out seating arrangements or something else, a structured approach and careful calculations are key to getting the right answer. Keep practicing, and you'll become a math whiz in no time!

In summary:

• The five four-person benches can hold 20 students.
• The two three-person benches can hold 6 students.
• The four benches that can seat four or five people can hold a maximum of 20 students.
• Total capacity: 46 students.
• The school cannot accommodate 50 students.

I hope this explanation was super helpful and made the problem easier to understand. If you have any more math questions, don't hesitate to ask! Until next time, keep crunching those numbers and have fun!