Athletes Race How To Calculate Finishers And Solve Math Problems
Hey guys, ever find yourself scratching your head over a seemingly simple math problem? Let's dive into a brain-teaser that involves a race, some dropouts, and a bit of logical deduction. We're going to break down this problem step by step, so you'll not only understand the solution but also the why behind it. So, buckle up, and let's get started!
Understanding the Race Scenario
Our main keywords here are athletes, race, finished, and total. Imagine a scenario: We have a race with a total of 10 athletes eager to cross the finish line. But, as it often happens in races, not everyone makes it to the end. Some drop out due to various reasons, like injury or exhaustion, while others might lag behind. In this particular race, we're told that 3 athletes had to drop out, meaning they didn't complete the race. Additionally, we know that 2 athletes finished in the last positions. This is crucial information, so let's hold onto it tightly as we proceed with solving the problem.
To truly grasp what's going on, it's helpful to visualize the race. Picture 10 runners at the starting line, each with the goal of completing the course. As the race progresses, some start to fall behind, and others might be forced to stop altogether. The challenge we face is figuring out exactly how many runners managed to push through and make it to the finish line, despite the setbacks faced by some of their competitors. Keep in mind, guys, this is not just about crunching numbers; it's about understanding the dynamics of the race and how each piece of information fits together.
Now, let's delve deeper into the specific details provided. The fact that 3 athletes dropped out is a straightforward subtraction from the total number of participants. However, the information about the 2 athletes finishing last requires a bit more thought. It tells us something about the finishers but doesn't directly give us the number of athletes who completed the race. It's like having pieces of a puzzle; we need to arrange them correctly to see the whole picture. So, with this race scenario firmly in mind, we're ready to start piecing together the solution. Remember, it's all about paying attention to the details and thinking logically. Let's move on to the next step in unraveling this athletic enigma!
Calculating the Number of Finishers
Now, let's get down to the nitty-gritty of calculating how many athletes actually finished the race. Our keywords here are calculate, finishers, athletes, and race. We started with a total of 10 athletes, right? But we know that 3 of them didn't make it to the finish line – they dropped out. So, the first step in our calculation is to subtract these dropouts from the total number of athletes. This gives us a clearer picture of how many athletes were still in contention to finish the race. Mathematically, we're doing this: 10 (total athletes) - 3 (dropouts). What does that give us? Seven athletes. This means that 7 athletes didn't drop out, but we're not done yet!
But here's where it gets a little tricky. We also know that 2 athletes finished in the last places. This might seem like extra information that doesn't matter, but it's actually a crucial piece of the puzzle. These 2 athletes did finish the race; they just weren't among the top finishers. They still crossed the finish line, which means they need to be included in our count of finishers. The key here is to recognize that finishing last still means finishing. It's a common point of confusion in these types of problems, so paying close attention to the wording is super important.
So, we know that we had 7 athletes who didn't drop out, and the question asks how many athletes completed the race. Since the 2 athletes who finished last did complete the race, we don't need to subtract them from our calculation. They are part of the group that finished. Therefore, the number of athletes who completed the race is actually 7. This is a classic example of how math problems can sometimes try to trick you with extra information, but if you break it down step by step, like we're doing, you can totally nail it. So, with this calculation in hand, we're one step closer to the final answer. But let's take a moment to think about why this makes sense in the context of the race. It reinforces the importance of thinking about the problem logically, not just mathematically. Let's move on and solidify our understanding of the solution!
Confirming the Solution Logically
Let's take a step back and logically confirm our solution. Our keywords here are confirm, solution, logically, and race. We've calculated that 7 athletes completed the race. Now, let's see if this makes sense in the grand scheme of things. We started with 10 athletes, 3 dropped out, and 2 finished in the last places. If 7 athletes finished, that means that 3 athletes did not finish the race. This aligns perfectly with the information given: 3 dropouts. So far, so good, guys!
Thinking about the race scenario, it's like visualizing the runners. Imagine 10 athletes starting, and then picture 3 of them stepping off the track before the finish line. That leaves 7 runners still in the race. Now, those 7 runners all cross the finish line, even though 2 of them come in last. The key is that they all finished. This logical visualization helps us avoid the common mistake of subtracting the last-place finishers from the total. It's a mental check that ensures our math aligns with the real-world situation. Math isn't just about formulas and equations; it's about understanding the story behind the numbers.
Another way to confirm our solution is to think about what it doesn't mean. If we had subtracted the 2 last-place finishers, we would have arrived at a different answer. But would that answer have made sense? No way! It would have meant that only 5 athletes finished, which wouldn't account for the 2 who finished last. So, by thinking critically about the implications of our answer, we can strengthen our confidence in the solution. This process of logical confirmation is super valuable in problem-solving. It's not enough to just get an answer; we need to be sure it's the right answer. So, with our logical check complete, we can confidently say that we're on solid ground. Let's move on to the final step: selecting the correct answer choice!
Selecting the Correct Answer Choice
Alright, we've crunched the numbers, we've thought it through logically, and now it's time to nail down the correct answer choice. The main keywords are selecting, correct, answer, and choice. Remember, the question asked us how many athletes completed the race, and we've determined that the answer is 7. Now, we just need to find the answer choice that matches our solution.
Looking at the options, we have: A) 5, B) 7, C) 8, and D) 10. It's clear as day, guys, that option B) 7 is the winner! This is the moment where all our hard work pays off. We've gone from understanding the problem to calculating the solution and then logically confirming it. Now, we can confidently select the correct answer and move on to the next challenge. But before we do, let's just take a moment to appreciate the process we've gone through.
This wasn't just about finding the number 7; it was about understanding why 7 is the answer. It's about developing problem-solving skills that you can apply to all sorts of situations, not just math problems. It's about breaking down complex information, thinking critically, and trusting your reasoning. So, as you approach future problems, remember the steps we took here: understand the scenario, calculate the solution, confirm it logically, and then confidently choose the answer. With these skills in your toolkit, you'll be unstoppable! And that's it, guys! We've successfully solved the problem and selected the correct answer choice. Let's keep this momentum going and tackle whatever comes our way!
How many athletes completed the race if, at the end, 3 of them dropped out and 2 finished in last place, considering that the race had a total of 10 athletes?
Athletes Race How to Calculate Finishers and Solve Math Problems
