Math Problem: Cost Of School Supplies
Hey guys, let's dive into a fun math problem today that involves some back-to-school shopping! We've got our friend Vasyl who's getting ready for the school year, and he's picked out a pencil case, a backpack, and four sketchbooks. He handed over a total of 60 UAH for all these goodies. Now, we know the pencil case set him back 12 UAH, and the backpack cost twice as much as the pencil case. The big question we need to crack is: how much did each of those four sketchbooks cost?
This is a classic word problem that tests our ability to break down information, perform simple calculations, and arrive at the final answer. It's the kind of problem you might encounter in elementary or middle school, and it's a great way to sharpen those problem-solving skills. We'll need to use a few steps to get there, starting with figuring out the cost of the backpack, then the combined cost of the pencil case and backpack, and finally, we can deduce the cost of the sketchbooks. Stick around, and we'll walk through it step-by-step, making sure everyone can follow along and understand the logic behind it. We're aiming to make math feel less like a chore and more like a puzzle we can solve together!
Breaking Down the Costs: Step 1 - The Backpack
Alright, so the first crucial piece of information we need to unlock is the cost of Vasyl's backpack. The problem states that he paid "у 2 рази більше, ніж за пенал" for his backpack, which translates to "2 times more than for the pencil case." We already know that the pencil case (пенал) cost him 12 UAH. To find the backpack's price, we simply need to multiply the pencil case's cost by two. So, that’s 12 UAH * 2 = 24 UAH. This means the backpack was a bit pricier than the pencil case, costing Vasyl 24 UAH. This is a key figure because it allows us to move closer to understanding the total expenditure on the main items before we even get to the sketchbooks. Understanding each component of the cost is vital in these types of problems. It’s like building blocks; you can't put the roof on before you have the walls. So, knowing the backpack cost 24 UAH is a significant step forward in solving our mystery of the sketchbook prices. We're building momentum here, guys!
Unveiling the Combined Cost: Pencil Case and Backpack
Now that we've figured out the cost of the backpack, let’s combine it with the cost of the pencil case. We know the pencil case cost 12 UAH, and we just calculated that the backpack cost 24 UAH. To find the total amount Vasyl spent on these two items, we add their costs together: 12 UAH + 24 UAH = 36 UAH. So, Vasyl spent a total of 36 UAH on his pencil case and backpack. This figure is super important because it represents a significant chunk of the total 60 UAH he paid. By subtracting this combined cost from the total amount he paid, we'll be able to determine exactly how much money was left for the four sketchbooks. This is where the puzzle really starts to come together, and we're getting closer to that final answer. It’s satisfying, right? Seeing how each piece of information leads us closer to the solution. Keep that total of 36 UAH in mind!
The Remaining Amount for Sketchbooks
We’re on the home stretch, folks! We know Vasyl paid a total of 60 UAH for everything. We've also calculated that the pencil case and backpack together cost 36 UAH. To find out how much money was left for the four sketchbooks, we simply subtract the combined cost of the pencil case and backpack from the total amount paid: 60 UAH - 36 UAH = 24 UAH. This means that Vasyl spent 24 UAH on all four of his sketchbooks. This is the total cost for all the sketchbooks combined. We're not quite done yet, as the question asks for the cost of each album (or sketchbook), but this 24 UAH is the critical number that will allow us to find that out. It’s like finding the treasure chest, and now we just need to count the coins inside!
Calculating the Cost Per Sketchbook
Finally, the moment we’ve been waiting for! We’ve determined that Vasyl spent a total of 24 UAH on four sketchbooks. The question asks for the cost of each sketchbook. To find this, we need to divide the total cost of the sketchbooks (24 UAH) by the number of sketchbooks (4). So, the calculation is: 24 UAH / 4 = 6 UAH. Therefore, each sketchbook cost Vasyl 6 UAH. Mission accomplished! We've successfully broken down the problem, used the given information, performed the necessary calculations, and arrived at the final answer. Each sketchbook cost 6 UAH. See? Math can be pretty straightforward when you tackle it step-by-step. It’s awesome when a plan comes together, right? So, next time you have a word problem, remember to break it down, find what you know, and figure out what you need to find. You got this!
Summary of Vasyl's Shopping Spree
Let's quickly recap Vasyl's shopping trip to make sure everything is crystal clear. He bought a pencil case for 12 UAH. His backpack cost twice that, so 12 UAH * 2 = 24 UAH. The total for these two items was 12 UAH + 24 UAH = 36 UAH. He paid a grand total of 60 UAH. The amount remaining for the four sketchbooks was 60 UAH - 36 UAH = 24 UAH. Since there were four sketchbooks, each one cost 24 UAH / 4 = 6 UAH. So, the final answer is that each album (sketchbook) cost 6 UAH. It’s always good to do a quick review to reinforce the steps and the answer. This method works for so many different types of problems. Keep practicing, and you'll be a math whiz in no time!
Why Word Problems Matter
Guys, understanding how to solve word problems like this one is super important. It's not just about getting the right answer; it’s about developing critical thinking and problem-solving skills that you can use in all parts of your life, not just in math class. When you break down a word problem, you’re learning to identify key information, ignore irrelevant details, and plan a strategy to reach a solution. This is a skill that's valuable whether you're trying to figure out how much paint you need for a room, how to budget your money, or even how to solve a complex issue at work. So, don't shy away from these problems! Embrace them as opportunities to train your brain to think logically and systematically. Every problem you solve makes you a little bit smarter and better equipped to handle whatever comes your way. Keep that brain power growing!