Solve: Missing Hotel Room Price?

Hey guys! Ever stumbled upon a problem that looks simple but makes you scratch your head a bit? Well, let's dive into one such puzzle today. We're going to break down a table showing hotel room prices and figure out a missing value. It's like being a detective, but with numbers! So, buckle up, and let's get started!

Understanding the Hotel Room Pricing Puzzle

Let's talk about this hotel room pricing puzzle. We've got a table that shows how the price changes depending on the number of nights you stay. Think of it as a mini-adventure in math, where we're trying to find a hidden treasure—the missing price! Now, to really nail this, we need to look closely at the numbers we already have. This isn't just about guessing; it's about spotting the pattern and using a little bit of math magic to reveal the answer. So, what exactly are we looking at? We have the prices for 1, 2, and 4 nights, but the price for 3 nights is playing hide-and-seek. Our mission, should we choose to accept it, is to find that missing piece. And trust me, it's more fun than it sounds! We're going to put on our math hats, sharpen our pencils (or, you know, open our favorite note-taking app), and get to work. Ready to become pricing puzzle pros? Let's do this!

Analyzing the Given Data: Spotting the Pattern

Okay, guys, let's put on our detective hats and really dig into this data. When we're trying to solve any math puzzle, the first thing we want to do is analyze the given data. Think of it like looking for clues in a mystery novel. What do we already know? We know the price for 1 night is $120, for 2 nights it's $240, and for 4 nights, it's $480. Now, the secret sauce here is to spot the pattern. Patterns are like the breadcrumbs that lead us to the solution. So, let's look closely: What's happening as the number of nights increases? Is the price going up by the same amount each time? This is where our inner mathematician comes out to play. We start comparing the numbers, doing a little mental math, and trying to see if there's a consistent relationship. Is it addition? Is it multiplication? Maybe it's something else entirely! By carefully examining the data points we have, we can start to form a hypothesis about what the missing value might be. It's like connecting the dots – each number is a dot, and the pattern is the line that connects them. So, let's keep those detective eyes peeled and see what we can uncover. The more closely we look, the clearer the solution will become. Let's find that pattern!

Identifying the Relationship: Multiplication in Action

Alright, team, let's roll up our sleeves and get to the heart of this. We've been looking at the data, and now it's time to identify the relationship between the number of nights and the price. Here's a hint: it involves multiplication! Remember how we talked about spotting patterns? Well, let's see how multiplication fits into the picture. If 1 night costs $120, what happens when we double the nights? We go to 2 nights, and the price doubles to $240. Interesting! What if we double the nights again? We jump to 4 nights, and the price doubles again to $480. Boom! A lightbulb should be going off right about now. It seems like each night adds another $120 to the total price. So, we're not just seeing a random set of numbers; we're seeing a consistent multiplication factor at play. This is like finding the secret code to unlock the puzzle. We've discovered that the price is directly related to the number of nights multiplied by a certain amount. But what amount? Well, we already know the answer: $120. Each night costs $120, and the total price is simply the number of nights times $120. This realization is huge because it gives us the key to finding the missing value. We're not just guessing anymore; we're using a proven relationship to calculate the answer. So, let's keep this multiplication magic in mind as we move forward. We're on the verge of cracking this case!

Calculating the Missing Value: The Math Behind It

Okay, mathletes, this is where the rubber meets the road. We've spotted the pattern, we've identified the relationship, and now it's time for the grand finale: calculating the missing value. Remember, we figured out that the price per night is a solid $120. So, if we know the number of nights, we can just multiply that by $120 to get the total price. Easy peasy, right? The missing value is the price for 3 nights. So, what's 3 multiplied by $120? Grab your calculators, or your mental math muscles, and let's crunch those numbers. 3 times $120 is… drumroll please… $360! Ta-da! We've found the missing piece of the puzzle. It's not just about pulling a number out of thin air; it's about using logic and math to arrive at the correct answer. And that's what makes it so satisfying. Now, we can confidently say that the price for 3 nights in this hotel is $360. We didn't just guess; we proved it with math. This is the power of understanding relationships and applying them to solve problems. So, let's give ourselves a pat on the back. We took on the challenge, we did the math, and we emerged victorious. But we're not done yet! Let's recap our journey and make sure we've got this concept down pat.

Verifying the Solution: Ensuring Accuracy

Alright, guys, we've found our missing value, but a good mathematician (or detective!) always verifies the solution. We want to make sure our answer makes sense and fits the pattern we've identified. So, let's put on our double-checking hats and give this another look. We calculated that the price for 3 nights is $360. Now, does this fit with the other prices we have? Let's see. We know 1 night is $120, 2 nights is $240, and 4 nights is $480. If we add $120 for each night, does it all line up? 1 night: $120. 2 nights: $120 + $120 = $240. 3 nights: $240 + $120 = $360. 4 nights: $360 + $120 = $480. Bingo! It all checks out. Our calculated value of $360 fits perfectly into the pattern. This is why verifying your solution is so important. It's like putting the final piece of a jigsaw puzzle in place – you can see the whole picture and know that everything is correct. It gives you confidence in your answer and shows that you've truly understood the problem. So, never skip this step! Whether you're solving a math problem or tackling any kind of puzzle, always take a moment to double-check your work. It's the key to accuracy and the mark of a true problem-solver. We've done it, guys! We've found the missing value and verified that it's correct. Now, let's wrap up our findings and celebrate our success!

Conclusion: Mastering the Art of Problem-Solving

Hey everyone, we did it! We successfully navigated the hotel room pricing puzzle, found the missing value, and verified our solution. But this wasn't just about finding a number; it was about mastering the art of problem-solving. We started by understanding the problem, then we analyzed the data, identified the relationship, calculated the missing value, and finally, verified our solution. These are the steps that can help you tackle any math problem, or any challenge in life, really. Think about it: we used our detective skills to spot patterns, we used our math skills to calculate the answer, and we used our critical thinking skills to verify our solution. These are powerful tools that you can use in all sorts of situations. And the best part? The more you practice, the better you get. So, don't be afraid to dive into puzzles and problems. Embrace the challenge, and remember the steps we've learned today. You've got this! And remember, math isn't just about numbers; it's about logic, reasoning, and problem-solving. It's a skill that can help you in so many ways. So, keep exploring, keep questioning, and keep solving. You're well on your way to becoming a problem-solving pro!

What is the missing value?

The missing value is the price for 3 nights, which we calculated to be $360.