Solving Mask And Hand Glove Price With Combined Method

by Scholario Team 55 views

Hey guys! Have you ever encountered a math problem that seems a bit tricky at first glance? Well, I've got one here that we can tackle together. It involves finding the prices of mask boxes and hand glove boxes using a combination method. Let's break it down step by step and make it super easy to understand.

Understanding the Problem

Before we dive into the solution, let's make sure we understand the problem clearly. We are given two scenarios:

  1. The price of 5 mask boxes and 3 hand glove boxes is Rp.360,000.00.
  2. The price of 4 mask boxes and 2 hand glove boxes is Rp.260,000.00.

Our goal is to find the price of 1 mask box and 1 hand glove box. To do this, we will use a combined method, which involves using the Least Common Multiple (LCM) and elimination. Trust me, it sounds more complicated than it actually is!

Setting Up the Equations

Okay, first things first, let's convert these statements into mathematical equations. This will make it easier for us to work with the numbers. Let's use:

  • M to represent the price of one mask box.
  • H to represent the price of one hand glove box.

Based on the information given, we can write two equations:

  1. 5M + 3H = 360,000
  2. 4M + 2H = 260,000

Now we have a system of two linear equations with two variables. This is a classic math problem that we can solve using several methods. Today, we're focusing on the combined method.

Finding the Least Common Multiple (LCM)

The next step is to find the Least Common Multiple (LCM) of the coefficients of one of the variables. In this case, let’s focus on the coefficients of H, which are 3 and 2. The LCM of 3 and 2 is 6. This means we want to manipulate our equations so that the coefficients of H in both equations become 6.

To do this, we'll multiply each equation by a suitable number:

  • Multiply the first equation by 2: 2 * (5M + 3H) = 2 * 360,000
  • Multiply the second equation by 3: 3 * (4M + 2H) = 3 * 260,000

After performing these multiplications, our equations become:

  1. 10M + 6H = 720,000
  2. 12M + 6H = 780,000

See how the coefficients of H are now both 6? We’re one step closer to solving this!

Elimination Method: Getting Rid of One Variable

Now comes the fun part – eliminating one of the variables. Since the coefficients of H are the same in both equations, we can subtract one equation from the other to eliminate H. Let's subtract the first equation from the second equation:

(12M + 6H) - (10M + 6H) = 780,000 - 720,000

This simplifies to:

2M = 60,000

Now we can easily solve for M:

M = 60,000 / 2 M = 30,000

So, the price of one mask box is Rp.30,000.00. Great job, guys! We've found one piece of the puzzle.

Finding the Price of a Hand Glove Box

Now that we know the price of a mask box (M), we can substitute this value into one of our original equations to find the price of a hand glove box (H). Let’s use the first original equation:

5M + 3H = 360,000

Substitute M = 30,000:

5 * 30,000 + 3H = 360,000

This simplifies to:

150,000 + 3H = 360,000

Now, let's isolate H:

3H = 360,000 - 150,000 3H = 210,000

Finally, solve for H:

H = 210,000 / 3 H = 70,000

So, the price of one hand glove box is Rp.70,000.00. Awesome! We've cracked it.

The Solution: Price of One Mask Box and One Hand Glove Box

Alright, we've done all the calculations, and here’s what we’ve found:

  • The price of one mask box (M) is Rp.30,000.00.
  • The price of one hand glove box (H) is Rp.70,000.00.

So, if you were to buy one mask box and one hand glove box, it would cost you Rp.30,000.00 + Rp.70,000.00 = Rp.100,000.00.

Why This Method Works: A Deeper Dive

Now, you might be wondering, why does this combined method work so well? Let’s break it down a bit further. The core idea is to manipulate the equations in such a way that we can eliminate one variable, making it easier to solve for the other.

The Power of LCM

Finding the LCM is crucial because it allows us to create equivalent equations where one of the variables has the same coefficient. By making the coefficients the same, we set the stage for easy elimination. Think of it like balancing scales – we're adjusting the equations so that they line up perfectly for the next step.

Elimination in Action

Elimination is where the magic happens. By subtracting one equation from the other, we effectively cancel out one variable. This leaves us with a single equation in one variable, which is super easy to solve. It’s like removing a distraction so you can focus on the main task.

Substitution: Completing the Puzzle

Once we’ve found the value of one variable, we use substitution to find the value of the other. Substitution is like filling in the missing piece of a puzzle. We take the value we've found and plug it into one of the original equations. This gives us a new equation that we can solve for the remaining variable.

Real-World Applications of This Method

This method isn't just useful for solving math problems in textbooks. It has practical applications in real life too! Here are a few examples:

Budgeting and Shopping

Imagine you're at the store and you know the total cost of two different combinations of items. You can use this method to figure out the individual prices of the items. This can help you make informed decisions about your purchases and stick to your budget.

Business and Finance

Businesses often use systems of equations to analyze costs, revenues, and profits. For example, they might use this method to determine the cost of raw materials and labor based on the total cost of producing different quantities of goods.

Science and Engineering

In science and engineering, systems of equations are used to model and solve a wide range of problems. From calculating the forces acting on a structure to determining the flow rates in a network of pipes, this method can be a powerful tool.

Tips for Mastering the Combined Method

Want to become a pro at using the combined method? Here are a few tips to help you along the way:

  1. Practice Makes Perfect: The more you practice, the more comfortable you'll become with this method. Try solving different problems with varying levels of difficulty.
  2. Stay Organized: Keep your work neat and organized. Write down each step clearly and label your variables. This will help you avoid mistakes and make it easier to review your work.
  3. Double-Check Your Answers: After you've found the solution, plug the values back into the original equations to make sure they hold true. This is a great way to catch any errors.
  4. Understand the Concepts: Don't just memorize the steps. Make sure you understand the underlying concepts. This will help you apply the method to different types of problems.
  5. Use Real-World Examples: Try to relate the problems to real-life situations. This will make the math more relevant and engaging.

Conclusion: You've Got This!

So, there you have it! We've successfully solved a problem involving mask boxes and hand glove boxes using the combined method. We've broken down the problem, set up equations, found the LCM, eliminated variables, and substituted values. You've learned a valuable skill that you can apply to many different situations.

Remember, guys, math might seem intimidating at first, but with a bit of practice and the right approach, you can conquer any problem. Keep exploring, keep learning, and keep having fun with math! You've got this! If you have any questions or want to try another problem, just let me know. Let’s keep the learning journey going!

Solve the problem: Given that the price of 5 mask boxes and 3 hand glove boxes is Rp.360,000.00, and the price of 4 mask boxes and 2 hand glove boxes is Rp.260,000.00, what is the price of 1 mask box and 1 hand glove box using the combined method (LCM 3 and 2, so LCM is 6, elimination)?

Solving Mask and Hand Glove Price with Combined Method