Solving Fish Purchase Problems: A Math Guide

by Dimemap Team 45 views

Hey guys! Ever been to a fish store and wondered how much each fish costs? Well, today, we're diving into a fun math problem involving Andra, Budi, Febri, Nana, and Putri at a fish shop. They're all buying different types of fish, and we'll use some algebra to figure out the price of each fish. This is a classic example of how math is super useful in everyday situations, even when it comes to buying fish. Let's break down the problem step-by-step to show you how easy it is! This is going to be a fun journey, so stick with me.

Understanding the Problem: The Fishy Situation

Alright, so here's the deal: Budi, Nana, and their friends are at a fish store. Budi buys 5 comet fish and 7 betta fish and spends Rp78,000.00. Nana gets 3 comet fish and 6 betta fish for Rp54,000.00. Our mission, should we choose to accept it (and we do!), is to figure out the individual cost of a comet fish and a betta fish. This is a classic word problem that can be solved using a system of linear equations. It's like a puzzle, and we're the detectives! We are going to solve this using systems of equations. It might sound scary, but trust me; it's not. We’ll use simple algebra to find our answers. The key is to break the problem into smaller, manageable parts. So, let’s begin our adventure!

This kind of problem is super common in algebra and shows you how to apply math to real-world scenarios. It's about translating a problem written in words into mathematical equations and then solving those equations. We'll use two variables: one for the cost of a comet fish and one for the cost of a betta fish. It's all about setting up these equations correctly, and then the solving part is relatively straightforward. I love how it breaks down complex situations into simpler parts. Let's start with the given data. We have information for Budi and Nana, but we'll soon include the rest as we uncover the secrets of the fish shop. Ready to begin? Let's go!

Setting Up the Equations: Translating Words into Math

Okay, time to get our math hats on! The first step is to turn the information we have into mathematical equations. Let's define our variables:

  • Let 'x' be the cost of one comet fish.
  • Let 'y' be the cost of one betta fish.

Now, let's translate Budi and Nana's purchases into equations:

  • Budi: 5 comet fish (5x) + 7 betta fish (7y) = Rp78,000.00. This gives us our first equation: 5x + 7y = 78,000.
  • Nana: 3 comet fish (3x) + 6 betta fish (6y) = Rp54,000.00. This gives us our second equation: 3x + 6y = 54,000.

See? It's all about translating the words into a mathematical language. These two equations form a system of linear equations, and we will solve them to find the values of x and y. Each equation represents the total cost of the fish purchased by Budi and Nana, respectively. Now, we're going to use the elimination method to solve this system. This method involves manipulating the equations so that one of the variables cancels out. It's one of the common methods to solve systems of equations.

It is so easy, right? This is the core of our problem. This step is about representing the problem in a way that allows us to find the answers using mathematical techniques. We're now set to start solving this. We're taking the real-world scenario and transforming it into something we can work with. Don't worry, even if you are not a math whiz, you can still follow along. By the end of this, you’ll be able to solve similar problems. Trust me; it's easier than it looks. We just have to be careful with the numbers and ensure we do everything correctly. This is the foundation upon which we will build our solution. It's really just a matter of practice.

Solving the Equations: Finding the Cost of Each Fish

Alright, let's get down to the solving part! We're going to use the elimination method. Here's how it works: first, we need to make the coefficients of either 'x' or 'y' the same in both equations. Let's eliminate 'x'. To do this, we'll multiply the first equation by 3 and the second equation by 5. This will make the coefficients of 'x' equal to 15.

  • (Equation 1 x 3): (5x + 7y = 78,000) * 3 => 15x + 21y = 234,000.
  • (Equation 2 x 5): (3x + 6y = 54,000) * 5 => 15x + 30y = 270,000.

Now, subtract the first new equation from the second new equation to eliminate 'x':

(15x + 30y) - (15x + 21y) = 270,000 - 234,000 9y = 36,000 y = 4,000

So, the cost of one betta fish (y) is Rp4,000.00. Next, we can substitute this value of 'y' back into either of the original equations to find the value of 'x'. Let's use the first original equation: 5x + 7y = 78,000.

5x + 7(4,000) = 78,000 5x + 28,000 = 78,000 5x = 50,000 x = 10,000

Therefore, the cost of one comet fish (x) is Rp10,000.00. Great job, guys! We've solved the equations. This part of the process is all about applying algebraic techniques to find the solutions. There are many ways to solve it, and the elimination method is just one of the effective methods. The most important thing here is not only knowing how to solve the problem but also why we are taking these steps. You will get more and more comfortable as you practice with similar types of problems. Remember, practice makes perfect. Now that we know the costs of both the comet fish and betta fish, we can move on.

Conclusion: Fish Costs Revealed!

So, to recap, here's what we found:

  • Comet Fish: Rp10,000.00 each.
  • Betta Fish: Rp4,000.00 each.

And there you have it! We've successfully used algebra to figure out the cost of each type of fish. It wasn't that tough, right? This problem demonstrates how math can be applied to everyday situations, making it fun and practical. Solving these kinds of problems helps improve your problem-solving skills and makes you more confident in using math. It also shows that math isn't just about abstract concepts. It's about tools that help us understand and solve real-world problems. Isn't that amazing? It gives us the power to understand and resolve so many things around us. Well done to you! You have successfully mastered this problem. Hope this helps you understand the concept better and boosts your confidence. Keep practicing and exploring the wonderful world of mathematics.

This is just one example of how math is used in everyday life. Whether you're at the store, planning a budget, or even just estimating how long it will take to get somewhere, math is always there! Feel free to ask more questions if you have them. I hope you enjoyed this guide to solving the fish purchase problem! Keep practicing your math skills, and you'll find that it's a valuable tool in many aspects of your life. Congratulations to all of you!