Finding The Price Of A Pen: A Simple Math Problem
Hey guys, let's dive into a classic word problem! This is a great example of how basic algebra can solve everyday scenarios, like figuring out the cost of school supplies. We'll break down the problem step-by-step, making it super easy to understand. So, grab your pencils and let's get started!
Understanding the Problem: What We Know
Okay, so the problem tells us that a shop sells 3 notebooks and 2 pens for a total of Rp 11,000. We also know that the price of one notebook is Rp 3,000. Our goal? To find out the price of a single pen. This is like a mini-mystery, and we're the detectives, gathering clues and solving the case! Before we jump into calculations, let's clarify what's being asked. We are tasked with figuring out the individual cost of a pen. It's crucial to understand this. You see, the scenario is like going to the store and knowing how much you spent overall, and the cost of some of the items, but needing to calculate the price of another item. So, by using the information provided, we can solve for the unknown price.
To solve this, we'll use a little bit of algebra, but don't worry, it's nothing complicated! It's all about setting up an equation that represents the problem. We can think of the total cost as the sum of the cost of the notebooks and the cost of the pens. That total cost is provided, making it easier to solve the problem. The price of the notebooks is easy to calculate because you know the price of one. This leaves us with only one unknown, the price of the pens. In this case, we have a total cost, and the price of one of the items in the total cost. By knowing these factors, we can set up an equation where one variable represents the unknown. This is a common way that these types of problems are written, so understanding how to work through them will definitely help you in the future! The problem is designed in a way that, by knowing the price of one item, you can solve for the unknown price of another item. Understanding this basic concept is key to working through these problems. Let's make sure we understand the whole setup before we dive into the calculations. This particular problem is set up in such a way that it can be easily solved with simple algebra.
We know the total cost, the individual cost of one item, and how many items are involved in both the total cost, and the individual cost. With these values, we can calculate the unknown price.
Setting Up the Equation: The Math Behind It
Alright, let's get mathematical! We can translate the problem into an equation. Let's use "x" to represent the price of one pen. Here's how we can set up the equation:
(3 * price of a notebook) + (2 * x) = Rp 11,000
We know the price of a notebook is Rp 3,000, so we can substitute that into the equation:
(3 * Rp 3,000) + (2 * x) = Rp 11,000
This is the core of our solution. This equation perfectly represents the situation described in the problem. The first part, (3 * Rp 3,000), represents the total cost of the notebooks. The second part, (2 * x), represents the total cost of the pens. And the whole thing equals the total cost, Rp 11,000. It's like a mathematical puzzle, where we are figuring out the cost of one item by knowing the total cost and the cost of other items. In this equation, we can use simple operations to figure out the value of x.
This is a good representation of a simple equation. It's like a balanced scale, where both sides must be equal. By keeping this balance, we can solve for the unknown variable. Equations like this are used everywhere in math and science. The ability to work through this is a useful tool that you can use in many different fields.
The cool thing is that, once you understand the equation, the rest is easy. It's all about isolating "x" to find its value. That is the only unknown in the equation. That is why it is so easy to solve. So, now, let's solve this equation.
Solving for x: Finding the Pen's Price
Now, let's solve for "x," which is the price of one pen. First, calculate the cost of the notebooks:
3 * Rp 3,000 = Rp 9,000
Our equation now looks like this:
Rp 9,000 + (2 * x) = Rp 11,000
Next, subtract Rp 9,000 from both sides of the equation to isolate the term with "x":
(2 * x) = Rp 11,000 - Rp 9,000
(2 * x) = Rp 2,000
Finally, divide both sides by 2 to find the value of x (the price of one pen):
x = Rp 2,000 / 2
x = Rp 1,000
So there you have it! The price of one pen is Rp 1,000. Awesome! We've successfully solved the problem using simple mathematical operations. You can double-check the work by multiplying the price of the pen by two, and adding it to the price of the three notebooks. The result of that should be the same as the total cost. Let's take a look at the answer and double-check.
Now we've got the solution! The individual price of one pen is Rp 1,000. To make sure, you can double-check it by calculating the total cost with the pen price.
Checking Our Answer: Does it Make Sense?
It's always a good idea to check your answer to make sure it makes sense. Let's see if our answer fits the original problem. We know:
- 3 notebooks cost 3 * Rp 3,000 = Rp 9,000
- 2 pens cost 2 * Rp 1,000 = Rp 2,000
Adding these together, Rp 9,000 + Rp 2,000 = Rp 11,000, which is the total cost given in the problem. So, our answer is correct! That means our solution works perfectly. If the equation isn't correct, it would not have equaled the provided total. Checking the answers is a crucial part of all problems, especially mathematical ones. You want to make sure the answer is accurate. That can be the difference between a high grade and a low grade!
This step is so important, because it assures that your answer is correct. If the answer doesn't match the original, then something went wrong during the calculation. It's always a great idea to make sure the calculations work out.
Conclusion: Problem Solved!
Congratulations, guys! We've successfully solved the problem and found the price of a pen. It's Rp 1,000. This example shows that even complex-looking problems can be solved with simple math and a logical approach. We used basic operations to find the value of x. By understanding the problem, setting up an equation, and carefully solving for the unknown, we found the answer! You can use this method to solve all sorts of similar problems. Pretty cool, right?
This is a good example of how these problems work. The most important thing is setting up the problem correctly. By understanding what is provided, and what you need to solve, you can get through any problem. It really is like solving a puzzle. Each clue will help you get to the answer. The ability to do this is one of the most useful skills you can develop.
Further Practice: More Problems to Try
Want to sharpen your skills? Try these similar problems:
- A store sells 2 apples and 4 bananas for Rp 8,000. If an apple costs Rp 1,500, what is the price of a banana?
- John buys 4 pencils and 1 eraser for Rp 7,000. If the eraser costs Rp 2,000, how much does one pencil cost?
These problems are very similar, so they will use the same steps. These are good examples to help you practice solving problems like these. With practice, you'll become a pro at these problems in no time! So, keep practicing and have fun!
If you want to practice your math skills, this is a great way to do it. The best way to get better is to keep practicing. So, find some similar problems and keep going. The more you work at it, the better you will get. Remember, it's all about practice! The more you practice, the easier these problems will become, and the more confident you'll feel when you face them.