Unraveling The Book Prices: A Math Challenge

by Dimemap Team 45 views

Hey guys! Let's dive into a fun math puzzle! Bаkyт went shopping and bought himself 4 books. Now, here's the kicker: The price of all the books without the first one is 42 soms, without the second, it's 40 soms, without the third, 38 soms, and without the fourth, 36 soms. The question is: How much does each book cost? Sounds interesting, right?

Decoding the Book Prices Mystery

Alright, so we've got a classic word problem here, perfect for flexing those math muscles! This isn't about complex formulas; it's more about logical thinking and setting up a simple equation to find the cost of each book. It involves setting up equations and solving for the unknown values. Let's break it down step by step to find out how to calculate each book price. The key is to understand how each piece of information relates to the others. We know the total cost without a specific book. This means we're essentially looking at the sum of the other three books in each scenario. By carefully comparing these sums, we can find out the price of each book.

Now, let's look at the information we have. First of all, we know that all the books without the first one cost 42 soms. We can denote the books as Book1, Book2, Book3, and Book4. Mathematically, it's like saying Book2 + Book3 + Book4 = 42. Next, the price of the books without the second one is 40 soms, that is Book1 + Book3 + Book4 = 40. Then, the total cost of the books, excluding the third book, is 38 soms, written as Book1 + Book2 + Book4 = 38. Finally, the sum of all books except the fourth is 36 soms, or Book1 + Book2 + Book3 = 36. So, we're basically looking for the individual price tags of each book. These numbers seem similar but not exactly the same, so there must be some difference in their costs, which is what we need to find out.

Let's use a systematic approach, which will involve creating and solving a system of equations, making the whole problem more understandable. We're going to use the information given to us, translating the descriptions into mathematical expressions and then manipulating those expressions to determine the unknown values. This is where your problem-solving skills come into play; it's kind of like being a detective, except instead of clues, we have numbers and equations. To ensure this goes smoothly, we need to create a plan before starting calculations. The initial step is to express the relationships described in the problem as a set of algebraic equations. Each equation represents the total cost of the books, excluding one, as mentioned in the question.

Step-by-Step Solution

Okay, let's get down to the real fun part: solving the puzzle! We will use the approach of solving systems of equations. To solve this problem, we're going to create a system of equations and manipulate them to find the price of each book. Each equation represents the total cost of the books minus one. First, let's denote the price of each book as follows: Book1 = B1, Book2 = B2, Book3 = B3, and Book4 = B4. Now, based on the information provided, we can write the following equations:

  • B2 + B3 + B4 = 42 (Equation 1)
  • B1 + B3 + B4 = 40 (Equation 2)
  • B1 + B2 + B4 = 38 (Equation 3)
  • B1 + B2 + B3 = 36 (Equation 4)

Now, let's solve these equations, so we can finally find the price of each book. One approach to solve it is to add all four equations together. By adding all four equations together, we get:

  • 3B1 + 3B2 + 3B3 + 3B4 = 42 + 40 + 38 + 36
  • 3(B1 + B2 + B3 + B4) = 156
  • B1 + B2 + B3 + B4 = 52 (Equation 5)

Equation 5 gives us the total price of all four books combined. This is a very important step to finding out the individual price of each book. Now, if we subtract each of the original equations from Equation 5, we can find out the price of each book individually. Let's do that:

  • Subtract Equation 1 (B2 + B3 + B4 = 42) from Equation 5 (B1 + B2 + B3 + B4 = 52): B1 = 10
  • Subtract Equation 2 (B1 + B3 + B4 = 40) from Equation 5 (B1 + B2 + B3 + B4 = 52): B2 = 12
  • Subtract Equation 3 (B1 + B2 + B4 = 38) from Equation 5 (B1 + B2 + B3 + B4 = 52): B3 = 14
  • Subtract Equation 4 (B1 + B2 + B3 = 36) from Equation 5 (B1 + B2 + B3 + B4 = 52): B4 = 16

Unveiling the Book Prices

Drumroll, please! After all that, we've cracked the code! The prices are as follows:

  • Book 1 costs 10 soms.
  • Book 2 costs 12 soms.
  • Book 3 costs 14 soms.
  • Book 4 costs 16 soms.

See, not that hard, right? This problem demonstrates a cool way to use systems of equations to solve real-life (or in this case, a book-buying) scenario. It’s all about breaking down the information into manageable parts and using logical steps to find the solution. The core of this problem lies in the clever use of equations. By carefully setting up and manipulating these equations, we can isolate each unknown value and find the price of each book. This approach not only provides the answers but also teaches us a valuable skill set in problem-solving.

Now, let’s quickly recap. First, we wrote out our given information as equations. Next, we added all the equations together to find the combined total. After that, we subtracted each original equation from the combined total. This let us isolate and solve for the price of each book. The method is efficient and elegant and shows the power of algebraic thinking in everyday scenarios.

Math in Everyday Life

This kind of problem-solving is super useful, guys! It’s all about the basic principles of mathematics. It is a fantastic way to sharpen your critical thinking abilities. You may not be buying books every day, but the skill of breaking down a problem into smaller parts and solving them is a great skill in a multitude of situations in our life. Whether it is calculating the cost of groceries or planning a budget, math is used everywhere. This puzzle is an excellent illustration of how math can be applied in simple, everyday situations, making it a very effective learning tool.

Beyond solving this specific problem, the approach used here – setting up equations and solving for unknowns – is a fundamental skill in many areas. Math provides the tools to solve a wide variety of problems, and the ability to interpret information, translate it into equations, and solve for unknowns is invaluable. As you work through more problems like this, you will become more comfortable with mathematical concepts. Each puzzle solved helps to build not just mathematical skills, but also to develop a more analytical mindset, which is beneficial in almost every aspect of life. Keep practicing, and you'll find that math can actually be fun and rewarding.

Final Thoughts

So there you have it, folks! We've solved the book price puzzle. It's a fun example of how math is not just about numbers; it's about thinking logically and applying the right tools to find a solution. The ability to break down complex problems into simple, manageable steps, and then to use mathematical tools to find the solution, is a skill that will serve you well in all aspects of life. Remember, practice is key, and every problem you solve makes you better at this game. Keep those math skills sharp, and don't be afraid to tackle new challenges!

I hope you enjoyed this math adventure! If you have any more puzzles or problems you'd like to solve, feel free to share. Happy problem-solving!