Fruit Price Puzzle: Solve Andi, Budi & Cici's Shopping Spree!

Hey everyone! Ever been stuck trying to figure out the cost of different fruits based on what your friends bought? Well, get ready to put on your detective hats because we're diving into a fun math puzzle! This is all about figuring out the price of apples, oranges, and pears. Let's get started with the problem: Andi bought 2 apples, 1 orange, and 1 pear for Rp 11,000. Budi got 1 apple, 2 oranges, and 1 pear for Rp 12,000. And finally, Cici picked up 1 apple, 1 orange, and 2 pears for Rp 13,000. Your mission, should you choose to accept it, is to match each fruit with its price using the provided options: Rp 2,000, Rp 3,000, and Rp 4,000. Ready to crack the code? Let's break it down and see if we can find the right prices for each fruit. This is a classic example of a system of equations, and we'll use a bit of logic and some clever calculations to solve it. Think of it like a fun game where you're the math superstar, and the fruits are the clues! We're going to work through this step by step, so don't worry if it seems a little tricky at first. By the end, you'll be a pro at solving these types of problems. Let's get started and see if we can find the prices of apples, oranges, and pears. This problem can be solved using a system of linear equations, which is a fundamental concept in algebra. The goal is to find the price of each fruit by setting up equations based on the purchases of Andi, Budi, and Cici. We have three equations with three unknowns (the prices of apples, oranges, and pears). Solving these equations simultaneously will give us the price of each fruit. This method is widely used in various fields, including economics, engineering, and computer science, to solve problems involving multiple variables and constraints. The process involves algebraic manipulation to isolate the unknowns and determine their values. So, are you ready to find out the value of each fruit?

Setting Up the Equations

Alright, guys, let's turn this shopping spree into a mathematical equation. We're going to use the information about what Andi, Budi, and Cici bought to create a system of equations. This is like building the foundation of our puzzle, so pay close attention! Let's start by assigning variables to the prices of each fruit: Let's say: * A = Price of an apple * O = Price of an orange * P = Price of a pear Now, we can translate what each person bought into an equation: * Andi: 2A + 1O + 1P = 11,000 * Budi: 1A + 2O + 1P = 12,000 * Cici: 1A + 1O + 2P = 13,000 See? We've turned words into math! Now, we have three equations and three unknowns, which means we can solve for the price of each fruit. This is where the fun begins! We're going to use these equations to figure out the individual prices of the apples, oranges, and pears. The system of equations can be solved using various methods, such as substitution, elimination, or matrix methods. Here, we will use a combination of elimination and substitution to find the price of each fruit. It's a bit like a puzzle where each step brings us closer to the solution. We're going to work through these equations carefully, so that we can solve it and find out the right value for each fruit! Let's see if we can solve them!

Solving the Equations: The Elimination Method

Now that we have our equations, it's time to roll up our sleeves and start solving them. We're going to use the elimination method, which is a clever way to get rid of some variables so that we can solve for others. Let's take our first two equations: 1. 2A + O + P = 11,000 2. A + 2O + P = 12,000 Notice that both equations have a + P. If we subtract the second equation from the first, we can eliminate P. So, we subtract the second equation from the first equation: (2A - A) + (O - 2O) + (P - P) = 11,000 - 12,000 This simplifies to: A - O = -1,000 Now we have a new, simpler equation! Let's keep that one in mind. We will also take the first and third equations: 1. 2A + O + P = 11,000 2. A + O + 2P = 13,000 Multiply the first equation by 2: 4A + 2O + 2P = 22,000 Subtract the third equation from this new equation: (4A - A) + (2O - O) + (2P - 2P) = 22,000 - 13,000 This simplifies to: 3A + O = 9,000 Alright, now we have two new equations: * A - O = -1,000 * 3A + O = 9,000 Add these together and we get: 4A = 8,000 Divide both sides by 4 to solve for A: A = 2,000 Great! The price of an apple is Rp 2,000. With this knowledge, let's find the price of the other fruits! Let's substitute this value back into the first equation and find O. Then we can use the value of A and O to find P. The elimination method is one of the most common and easiest ways to find the solution of the system of equations. Let's find the values of each fruit by using the knowledge we've gained.

Unveiling the Prices: Finding the Remaining Values

We've found the price of the apples. Now, let's keep the ball rolling and find out the price of oranges and pears! We know that A = 2,000. We can now substitute this value back into one of our simplified equations to find O. Let's use the equation A - O = -1,000. Substitute A = 2,000 into the equation: 2,000 - O = -1,000 Subtract 2,000 from both sides: -O = -3,000 Multiply by -1: O = 3,000 Awesome! The price of an orange is Rp 3,000. Now that we know A = 2,000 and O = 3,000, we can use one of the original equations to find P. Let's use Andi's equation: 2A + O + P = 11,000 Substitute A and O: 2(2,000) + 3,000 + P = 11,000 Simplify: 4,000 + 3,000 + P = 11,000 Combine like terms: 7,000 + P = 11,000 Subtract 7,000 from both sides: P = 4,000 Ta-da! The price of a pear is Rp 4,000. So, we've solved the puzzle! The prices are: * Apple: Rp 2,000 * Orange: Rp 3,000 * Pear: Rp 4,000 We successfully figured out the prices of each fruit by carefully setting up and solving the equations! It was a fun journey, wasn't it? These types of problems help us improve our problem-solving skills. The use of algebraic manipulation can be applied to many real-world scenarios. This method can also be used for more complicated scenarios. With this knowledge, we are ready to answer the main question.

Matching Fruits to Prices

Now that we have all the prices, let's match them up with our options: * Rp 2,000: Apple * Rp 3,000: Orange * Rp 4,000: Pear There you have it! We successfully found the price of each fruit and matched them to the correct amounts. This math problem was a fun way to practice solving a system of equations, right? We used logic, combined equations, and found the right price for each fruit. This demonstrates how math can be used to solve everyday problems. These types of puzzles are very useful and can be applied in real life! Remember, it’s all about breaking down the problem, setting up your equations, and solving them step by step. Math is not only about numbers; it's a tool that can help you to think logically and strategically. You've done a great job! Keep practicing, and you'll become a math superstar in no time. Always remember the steps to solve the problem: setting up the equations, using methods such as substitution or elimination, and finding the final answer. This is a skill that you can use everywhere!

Conclusion

Congrats, you've successfully solved the fruit price puzzle! We started with the purchases of Andi, Budi, and Cici, turned those into equations, and used the elimination method to find the price of each fruit. This problem demonstrates how useful math can be in everyday life, from figuring out shopping costs to analyzing data and solving complex problems. Always remember to break down complex problems into smaller parts. With each step, you are getting closer to the answer! With the values we've found, we can now go and shop for fruits without having to think so hard about the price. The use of algebra and mathematics provides a framework for modeling and solving real-world problems. This can be applied in many fields. I hope you enjoyed this math adventure, guys! Keep practicing, keep exploring, and keep having fun with numbers!