Menghitung Harga Buku & Pensil: Solusi Matematika Lengkap

by Tim Redaksi 58 views
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Hey guys! Let's dive into a fun math problem that's super practical for everyday life. We're going to figure out the cost of books and pencils based on some clues. It's like being a detective, but instead of solving a mystery, we're solving a price puzzle! This is a great example of how algebra can be used in real-world situations, making it a valuable skill to have. So, grab your notebooks and let's get started. The core of this problem revolves around understanding how to set up and solve simultaneous equations. These equations will help us to find the individual prices of a book and a pencil, which will then enable us to calculate the total cost for a specific quantity of each item. This approach not only showcases mathematical principles but also highlights the usefulness of mathematical problem-solving in everyday financial planning. It's a great exercise in critical thinking, perfect for sharpening your skills and making you more confident in tackling similar problems in the future. We'll break down each step so it's easy to follow. Remember, practice makes perfect, and the more you work through these types of problems, the better you'll become!

This kind of problem is common in mathematics, especially in algebra. The ability to translate a word problem into a set of equations and then solve them is a fundamental skill. It not only helps with math exams but also develops the ability to analyze and solve problems in various areas of life. The problem itself seems simple, yet the method to solve it has applications in economics, business, and even science. The key is to break down the information, identify the unknowns, and use the provided relationships to find the answers. This method, applied to different scenarios, can prove extremely useful in managing budgets, calculating costs, and making informed decisions. By understanding this process, we can gain a clearer understanding of how mathematics can be applied to real-world financial problems. So, get ready to stretch your mental muscles and let's get started!

Memahami Soal: Apa yang Kita Ketahui?

Alright, let's break down what we already know. The problem gives us two important pieces of information:

  1. The cost of 4 books and 3 pencils is Rp.2.500,00.
  2. The cost of 2 books and 7 pencils is Rp.2.900,00.

Our mission, should we choose to accept it (and we do!), is to find out the cost of 2 dozen books (24 books) and 4 dozen pencils (48 pencils). This is a classic example of a linear equation problem. We're dealing with the price of books and pencils, both of which have a linear relationship with the quantity. Understanding these relationships is fundamental to grasping the concept of algebra. By working through this problem, we'll gain a deeper appreciation for how mathematical concepts can be applied in everyday scenarios. The goal here isn't just to get the answer, but to understand the method so you can tackle similar problems with confidence. It is really important to grasp these concepts to deal with more complex mathematical challenges. Remember, every step we take strengthens our mathematical muscles and brings us closer to mastering these vital concepts. This kind of logical reasoning can also boost your problem-solving skills across various fields, not just math!

So, before we even start, let's make sure we're on the same page. We're not just solving for x and y; we're figuring out the real-world prices of items you might buy at a bookstore. This makes the whole process more relatable and less abstract. It's a great example of how math is more than just numbers; it's about making sense of the world around us. Let's make sure we have a solid understanding of each step.

Menyatakan Informasi dalam Bentuk Persamaan

Okay, time to turn words into equations! Let's represent the price of a book with the variable "b" and the price of a pencil with the variable "p". Based on the information given, we can create two equations:

  1. 4b + 3p = 2500 (This represents the cost of 4 books and 3 pencils).
  2. 2b + 7p = 2900 (This represents the cost of 2 books and 7 pencils).

These equations are the core of our problem. They allow us to use the power of algebra to find out the individual costs of a book and a pencil. Setting up these equations is critical because it transforms the word problem into a mathematical format that's easier to solve. Now, it's not just about memorizing formulas, but about understanding how to translate real-world scenarios into equations. This is where the true power of mathematics shines. This is a very common task in mathematical problem-solving, which has wide implications in fields like economics, business, and science. The ability to convert a word problem into equations is a key skill.

We'll use these equations to find the value of "b" and "p". Think of it as decoding a hidden message. Each equation gives us a clue, and by combining them, we can unlock the secrets to finding the prices. The more comfortable you get with setting up these equations, the easier it will become to solve more complex problems. Remember, the goal here is to understand the process. The process is much more important than the final numbers, because it's the process that builds your confidence and skills. Let's keep moving and you'll see how it all comes together!

Menyelesaikan Persamaan: Menemukan Harga Buku & Pensil

Now for the fun part: solving the equations! There are several methods to solve these simultaneous equations, but we'll use the elimination method because it's straightforward. This method involves manipulating the equations so that we can eliminate one of the variables. By doing this, we can solve for the remaining variable. Remember, the goal is to get closer to the final answers. So, stick with it! This method is a great example of how mathematical principles can be applied to real-world situations, making it a valuable skill to have. We'll break down each step.

Langkah-langkah Eliminasi

  1. Multiply Equation 2 by 2: This gives us 4b + 14p = 5800. We do this so that the coefficient of "b" in both equations becomes the same, which will allow us to eliminate "b" later.
  2. Subtract Equation 1 from the new Equation 2: This means (4b + 14p) - (4b + 3p) = 5800 - 2500. This simplifies to 11p = 3300.
  3. Solve for p: Divide both sides by 11 to get p = 300. So, the price of a pencil is Rp.300,00.
  4. Substitute p into either original equation to find b: Let's use 4b + 3(300) = 2500. This simplifies to 4b + 900 = 2500. Subtract 900 from both sides: 4b = 1600. Then, divide by 4: b = 400. So, the price of a book is Rp.400,00.

That was pretty cool, right? Using the elimination method, we've successfully found the prices of both a book and a pencil. This part of the process illustrates the beauty and power of mathematical problem-solving. This is the heart of the algebraic method. Each step has brought us closer to the final solution. The more you practice these techniques, the more natural and confident you will become in dealing with similar problems. This method isn't just useful for this problem; it's a valuable skill that applies to a variety of situations. Remember, the key is to understand the underlying principles.

Menghitung Harga 2 Lusin Buku & 4 Lusin Pensil

We're almost there, guys! Now that we know the price of a book (Rp.400,00) and a pencil (Rp.300,00), we can calculate the cost of 2 dozen books and 4 dozen pencils.

  • 2 dozen books is 2 x 12 = 24 books.
  • 4 dozen pencils is 4 x 12 = 48 pencils.

So, the total cost will be: (24 books x Rp.400,00) + (48 pencils x Rp.300,00). It is easy to see how the mathematical skills we've learned can be directly applied to calculate costs in our daily lives. This calculation is a clear example of applying mathematical skills to real-world situations.

Perhitungan Akhir

Let's do the final calculation:

  • Cost of 24 books = 24 x Rp.400,00 = Rp.9.600,00
  • Cost of 48 pencils = 48 x Rp.300,00 = Rp.14.400,00
  • Total cost = Rp.9.600,00 + Rp.14.400,00 = Rp.24.000,00

Therefore, the price of 2 dozen books and 4 dozen pencils is Rp.24.000,00! Woohoo! We did it! This is a great example of how mathematical principles can be applied to real-world situations, making it a valuable skill to have. Now, you can apply this process to other problems, from budgeting your pocket money to planning larger expenses. And remember, the key to success in math, like anything else, is practice. The more problems you solve, the more confident and skilled you'll become. So, keep practicing and keep exploring the amazing world of mathematics! The ability to solve these kinds of problems is useful in a variety of fields, and the skills you develop are really valuable.

Kesimpulan

So there you have it, guys! We've successfully navigated the math maze and solved the problem. We started with a set of clues and used our algebra skills to find the prices of books and pencils. From there, we calculated the total cost of a larger quantity. This whole process shows how essential math is in our daily lives, from managing finances to making informed decisions. By practicing these types of problems, we strengthen our problem-solving abilities and our understanding of mathematical concepts. Remember, the key is to break down the problem into smaller parts, understand the underlying principles, and use the tools at your disposal. The more you practice, the easier it will become. Keep up the great work and keep exploring the world of mathematics. The ability to use math to solve problems like this is a valuable skill in many aspects of your life. This method can also be used to solve different types of problems, not only in academics but also in day-to-day life. So, well done!