Solving A Wheat Sack Problem Step-by-Step Math Challenge

by Scholario Team 57 views

Hey guys! Let's tackle this interesting math problem together. We're going to break down how to solve a classic problem involving two sacks of wheat. The problem states that two sacks contain a total of 142 kg of wheat. One sack holds 28 kg more than the other. Our mission, should we choose to accept it, is to figure out how many kilograms of wheat are in each sack. Sounds like a fun challenge, right? Let's dive in!

Understanding the Problem

So, when we're dealing with word problems, the first step is always to make sure we really get what's going on. Understanding the problem is half the battle, trust me! In this case, we've got two sacks, and they don't have the same amount of wheat. One's heavier, carrying an extra 28 kg. The key piece of info is the total weight: 142 kg. We need to find two separate weights that add up to 142 kg, with a 28 kg difference between them.

Why is this important? Because if we jump straight into calculations without fully grasping the situation, we might end up with the wrong answer. Think of it like trying to build a house without reading the blueprint first – you might end up with some wonky walls! So, let's make sure our foundation is solid before we start adding numbers.

Let's recap: We have:

  • Total weight: 142 kg
  • Weight difference: 28 kg
  • Goal: Find the individual weight of each sack

Now that we've got a clear picture, let's move on to the next step: figuring out how to actually solve this thing. Stay with me, guys, we're getting there!

Setting up the Equations

Alright, guys, let's get a little mathematical! To solve this problem, we're going to use something called algebra. Don't worry if that word sounds intimidating – it's just a fancy way of using symbols to represent unknown numbers. In our case, we don't know the weight of each sack, so we'll use letters to stand for those weights. This is a crucial step in problem-solving because it helps us translate the word problem into a mathematical language we can work with.

Let's say:

  • The weight of the first sack is represented by the letter 'x'.
  • Since the second sack contains 28 kg more than the first, we can represent its weight as 'x + 28'.

Now, we know that the total weight of both sacks combined is 142 kg. So, we can write this as an equation:

x + (x + 28) = 142

See how we've turned our word problem into a neat little equation? This is the power of algebra! We've now got a mathematical sentence that describes the situation. Why is this so cool? Because we have established a solid mathematical framework, we can use mathematical rules to solve for 'x'. This equation is the key to unlocking the answer.

Now, before we start solving, let's just take a moment to appreciate what we've done. We've taken a real-world scenario and translated it into the language of math. That's a pretty awesome skill to have!

Solving the Equation

Okay, guys, we've got our equation: x + (x + 28) = 142. Now comes the fun part – actually solving it! Don't worry, it's not as scary as it looks. We're going to take it step by step. The goal here is to isolate 'x' on one side of the equation, which means getting 'x' by itself.

First, let's simplify the equation by combining the 'x' terms:

x + x + 28 = 142 becomes 2x + 28 = 142

See? We've made it a little cleaner already. Now, we want to get rid of that '+ 28' on the left side. To do that, we'll subtract 28 from both sides of the equation. Why both sides? Because in math, what you do to one side, you have to do to the other to keep things balanced. Think of it like a scale – if you take weight off one side, you need to take the same weight off the other to keep it even.

So, we have:

2x + 28 - 28 = 142 - 28 which simplifies to 2x = 114

We're getting closer! Now we have '2x', but we just want 'x'. What's the opposite of multiplying by 2? Dividing by 2! So, we'll divide both sides of the equation by 2:

2x / 2 = 114 / 2 which gives us x = 57

Boom! We've solved for 'x'! That means the first sack contains 57 kg of wheat. But we're not done yet – we still need to find the weight of the second sack.

Finding the Weight of Each Sack

Alright, mathletes, we've cracked the code and found that x = 57. Remember, 'x' represents the weight of the first sack. So, the first sack contains a solid 57 kg of wheat. But what about the second sack? Don't forget, we said the second sack contains 'x + 28' kilograms. This is a crucial step because stopping here would only give us half the answer! Why? Because the problem specifically asks for the weight of each sack.

To find the weight of the second sack, we simply substitute the value of 'x' (which is 57) into our expression 'x + 28':

Weight of second sack = 57 + 28

Let's do the math:

57 + 28 = 85

So, the second sack contains 85 kg of wheat. Woohoo! We've found the weight of both sacks. But before we do a victory dance, there's one more important step we need to take.

Checking the Answer

Okay, guys, we've done the hard work, but we're not quite at the finish line yet! The final, crucial step in any problem-solving endeavor is to check our answer. Why is this so important? Because it's super easy to make a small mistake along the way – a dropped sign, a miscalculation, you name it. Checking our answer is like proofreading an essay or double-checking your GPS directions before a road trip. It helps us catch any errors and make sure we're on the right track.

In this case, we have two key pieces of information we can use to verify our solution:

  1. The total weight: The two sacks should add up to 142 kg.
  2. The weight difference: One sack should weigh 28 kg more than the other.

Let's see if our answers hold up. We found that the first sack weighs 57 kg and the second weighs 85 kg.

  • Total weight: 57 kg + 85 kg = 142 kg. Bingo! Our total weight checks out.
  • Weight difference: 85 kg - 57 kg = 28 kg. Double bingo! The weight difference is also correct.

Since both conditions are satisfied, we can confidently say that our answer is correct. We've successfully found the weight of each sack of wheat!

Final Answer

Alright, guys, we've reached the end of our mathematical journey! Let's recap our solution and give the final answer in a clear and concise way. Remember, communication is key in math (and in life!). It's not enough just to find the answer; we need to be able to explain it to others.

Here's our final answer, stated clearly:

  • The first sack contains 57 kg of wheat.
  • The second sack contains 85 kg of wheat.

We've successfully solved the problem! We started by understanding the situation, then we set up an equation, solved it step by step, and finally, we checked our answer to make sure we were right. That's the problem-solving process in action!

So, what have we learned today? We've learned how to tackle a word problem involving two unknowns. We've seen how algebra can be a powerful tool for solving real-world scenarios. And most importantly, we've learned the importance of checking our work. Math isn't just about getting the right answer; it's about understanding the process and being confident in our solution.

Great job, everyone! You guys are math rockstars! Keep practicing, keep exploring, and keep challenging yourselves. Math can be fun, and it's definitely a skill that will serve you well in all areas of life. Until next time, keep those brains buzzing!