Nafisa & Jamila's Money: Solving A Sum Problem!

Hey guys! Let's dive into a fun math problem involving Nafisa and Jamila's money. This is a classic example of how we can use algebra to solve real-world scenarios. We're going to break down the problem step by step, making it super easy to understand. So, grab your thinking caps, and let's get started!

Problem Setup: Understanding the Initial Conditions

So, the main keyword here is understanding the initial conditions of Nafisa and Jamila’s money. We know that Nafisa initially had 18,000 sum more than Jamila. Let's represent Jamila's initial amount of money as 'x'. That means Nafisa's initial amount would be 'x + 18000'. This sets the foundation for our algebraic equations. It's crucial to visualize this difference clearly before moving forward. Imagine Nafisa having a bigger pile of money than Jamila – that's the 'x + 18000' versus 'x'. These initial amounts are the starting point, and the subsequent changes will affect their relative values. Think of it like this: if Jamila had 10,000 sum, Nafisa would have 28,000 sum. This initial difference is key to solving the problem correctly. We have to be precise with these definitions; otherwise, everything else falls apart! This part is more than just stating facts; it's about painting a picture and creating a mental model that makes the problem less abstract. Without this understanding, the equations will just look like random symbols. So, take a moment to really grasp the starting amounts. Are we clear on how Nafisa's initial money is related to Jamila's? Once you have that down, the rest is much easier to follow. This part is the bedrock upon which we build the solution. Don't rush through it! In summary, Nafisa's money is Jamila's money plus 18,000 sum. Simple as that.

Changes: Mother's Contribution

Now, the keyword to focus on is the impact of the mother's contribution. Their mother gave Nafisa 4,000 sum and Jamila 6,000 sum. This means we need to update their amounts. Nafisa now has 'x + 18000 + 4000' sum, and Jamila has 'x + 6000' sum. It’s important to keep track of these additions. These additions change the initial amounts, and that will affect the relationship between the money they have. Think of it like adding ingredients to a recipe – it changes the final dish. So, Nafisa's amount has increased, but so has Jamila's. The key question is, how did this change their relative amounts? Did it close the gap or widen it? It's not just about knowing the numbers; it's about understanding the implications of those numbers. We have to be careful to add the correct amounts to the correct people. A simple mistake here will throw off the whole calculation. So, double-check your work. Make sure you are adding 4,000 to Nafisa's total and 6,000 to Jamila's total. This step is crucial for setting up the equation correctly. By carefully accounting for the mother's contribution, we can see how the amounts of money have changed from their initial values. So, let’s keep going and make sure we have a clear understanding of everything before moving on. Keep in mind that this is just about accurately reflecting the described scenario mathematically.

The Key Relationship: Jamila's Money is Half of Nafisa's

This section is all about Jamila's money being half of Nafisa's money, which is the pivotal piece of information. After the mother's contributions, Jamila's money became half of Nafisa's money. This can be written as an equation: x + 6000 = 0.5 * (x + 18000 + 4000). This equation is the heart of the problem. It translates the verbal relationship into a mathematical statement. Now, we can use algebra to solve for 'x'. This equation is where we connect all the pieces. It tells us exactly how Jamila's money relates to Nafisa's after all the changes. So, understanding this relationship is crucial for getting the right answer. If we don't have the correct equation, we're dead in the water. So, we need to examine the equation closely and make sure it makes sense in the context of the problem. This equation is a statement of equality – it says that the two sides of the equation are equal. The left side represents Jamila's money, and the right side represents half of Nafisa's money. If the problem stated that Jamila's money was one-third of Nafisa's, the '0.5' would become '0.333'. So, the equation is a flexible tool that can adapt to different scenarios. So, let’s move on and make sure that all of our calculations are correct. Once we find the value of x, we will be closer to the final answer.

Solving for 'x': Finding Jamila's Initial Money

Now, let's focus on solving for 'x' to find Jamila's initial money. First, we simplify the equation: x + 6000 = 0.5 * (x + 22000). Next, distribute the 0.5: x + 6000 = 0.5x + 11000. Then, subtract 0.5x from both sides: 0.5x + 6000 = 11000. Finally, subtract 6000 from both sides: 0.5x = 5000. Divide by 0.5: x = 10000. Therefore, Jamila initially had 10,000 sum. This is a critical milestone in solving the problem. We have found the value of 'x', which represents Jamila's initial amount. But we're not done yet! We still need to find Nafisa's initial amount. It’s super important that we follow all of the correct algebraic steps to find the correct value of x. Also, remember to do the same steps to both sides of the equation. In fact, a good way to double-check your work is to enter the value of x back into the original equation and see if it balances. If both sides of the equation are equal, then you know you have the correct answer. Once we get this right, we can find the value of all the other variables. So, double-check your math! The algebraic manipulation must be accurate. We can't stress this enough! A small error in arithmetic can lead to a wildly incorrect answer. This is a classic example of why attention to detail is important in math. Think of it like building a house – if the foundation is not solid, the whole structure will be unstable. In this case, the value of 'x' is the foundation upon which we build the rest of the solution. So, let's take a deep breath, review our steps, and make sure we have the right value. After all, we want to get this problem right! Okay, we've solved for 'x'. Excellent work, guys! Let’s keep going!

Finding Nafisa's Initial Money

The keyword is finding Nafisa's initial money. Since Nafisa had 18,000 sum more than Jamila initially, Nafisa had 10000 + 18000 = 28,000 sum. Now we know how much each of them had originally. Remember that at the beginning, we defined Nafisa's initial amount as 'x + 18000'. Now that we know 'x' is 10,000, we just add 18,000 to get 28,000. It's as simple as that! But let's not take anything for granted. It's always a good idea to double-check our work, especially when we're dealing with multiple steps. So, let's ask ourselves, does it make sense that Nafisa had 28,000 sum initially? Well, the problem stated that she had 18,000 sum more than Jamila, and we found that Jamila had 10,000 sum. So, 28,000 is indeed 18,000 more than 10,000. So, it checks out! We can be confident that we have the correct value for Nafisa's initial amount. This step is crucial for completing the problem. We can't just stop at finding Jamila's initial amount. We need to find both amounts to fully answer the question. So, make sure you always read the problem carefully and understand what it's asking for. In this case, it's asking for the initial amounts of both Nafisa and Jamila. We've found both amounts, so we're almost there! One more step to go. The key takeaway here is to always go back to the original problem and make sure you're answering the question that was asked. It's a common mistake to stop too early, especially when you're under pressure. So, take a deep breath, stay focused, and make sure you're answering the right question. Let’s keep going!

Final Answer: Stating the Solution Clearly

Now, for the final keyword: stating the solution clearly. Initially, Nafisa had 28,000 sum, and Jamila had 10,000 sum. This is the complete answer to the problem. We have solved for 'x', found Nafisa's initial amount, and double-checked our work. Now we can confidently state the solution clearly and concisely. It's important to present the answer in a way that is easy to understand. Avoid using any jargon or complicated language. Just state the facts clearly and directly. In this case, the facts are that Nafisa had 28,000 sum and Jamila had 10,000 sum. It's also a good idea to include the units in your answer. In this case, the units are 'sum'. So, make sure you include the units to avoid any ambiguity. When you state the final answer, remember to clearly separate the two amounts. This makes it easy for the reader to see the solution. You can use a sentence, a bullet point list, or any other method that is clear and concise. The goal is to communicate the solution effectively. That's it, guys! We've solved the problem! We found that Nafisa initially had 28,000 sum and Jamila had 10,000 sum. We have taken into account all the information given in the problem and have successfully found the answer. Be sure to review all the steps to improve your understanding, and now you can tackle similar problems with confidence! Great job, everyone!