Solving Ellen's Money Problem: A Math Word Problem

Let's dive into a classic math problem! We're going to break down a word problem step-by-step, making it super easy to understand. We’ll focus on Ellen's shopping trip and figure out how much money she has left. So, if you're ready to sharpen those math skills, let's get started, guys!

Understanding the Problem

In this section, we will deeply understand the problem, the crucial first step in solving any math challenge. To solve math problems effectively, especially word problems, it is very important to grasp what the problem is asking. Underlining important information and defining the question to be answered are key strategies here.

So, let's break it down. The problem states: Ellen initially had P700. She made two purchases: a cassette tape costing P120 and a T-shirt costing P450. The main question we need to answer is: How much money does Ellen have remaining after these purchases? This is the core of the problem, and identifying it clearly helps us to focus on the steps needed to find the solution. The underlying mathematical concept here involves subtraction because Ellen is spending money, which reduces her initial amount. This understanding helps in choosing the correct operation to use.

To ensure clarity, it is often helpful to rephrase the question in your own words. For instance, we can restate the question as, "What is the difference between Ellen's initial money and the total amount she spent?" This restatement reinforces our understanding and prepares us for the next steps in solving the problem. By pinpointing the question and the core concept involved, we set a strong foundation for accurately calculating the answer. Remember, a clear understanding of the problem is half the solution!

Identifying the Operation

Now, let’s talk about figuring out what math to use. Identifying the correct mathematical operation is a critical step in solving word problems. In Ellen's case, she started with a certain amount of money and then spent some. This key action of spending indicates that we need to use subtraction. When you spend money, you're taking away from your total, right? That's exactly what subtraction does.

The problem involves two transactions where Ellen spends money: first on a cassette tape and then on a T-shirt. To determine the total amount she spent, we need to combine these amounts. This combining action tells us we also need to use addition. So, we have a two-step process here: first, add the amounts Ellen spent, and then subtract that total from her initial amount. Thinking through the actions described in the problem—spending and combining—helps us logically connect these actions to the correct math operations.

Keywords within the problem can also provide hints about the operation needed. For instance, phrases like "how much left," "spent," and "difference" often suggest subtraction. Conversely, words like "total" or "altogether" typically indicate addition. Recognizing these keywords can act as a guide, particularly in more complex problems. By logically analyzing the scenario and noting these keywords, you can confidently select the correct operations to solve the problem. In Ellen's case, subtraction is key to finding the remaining amount, but addition plays a supporting role in calculating the total expenditure.

Writing the Mathematical Sentence

Let's translate the problem into a math sentence! Turning a word problem into a mathematical sentence is like creating a roadmap for solving it. It's a concise way to represent all the information and operations needed. For Ellen's situation, we start with her initial amount, which is P700. Then, we know she spent P120 on a cassette tape and P450 on a T-shirt. We need to subtract these amounts from her initial money.

The mathematical sentence will represent this series of actions. First, we can represent the total amount spent by adding the cost of the cassette tape and the T-shirt, which is P120 + P450. Then, we subtract this total from the initial amount of P700. Therefore, the complete mathematical sentence is: P700 - (P120 + P450) = ?. This sentence clearly shows the order of operations: we first add the amounts in the parentheses and then subtract the result from P700.

Writing the mathematical sentence not only clarifies the steps but also helps in organizing the calculations. The use of parentheses is crucial here because it indicates that the addition should be performed before the subtraction, following the mathematical order of operations. This structured approach minimizes errors and makes the solution process more straightforward. By accurately writing the mathematical sentence, we set the stage for a correct and efficient calculation of the final answer. It's like having the blueprint before starting construction!

Calculating the Answer

Alright, time to do the math and find the final answer! Now that we have our mathematical sentence, P700 - (P120 + P450) = ?, we can proceed with the calculations. Remember, the order of operations is crucial here, so we start with what's inside the parentheses.

First, we add the cost of the cassette tape and the T-shirt: P120 + P450. When we add these two amounts together, we get P570. This is the total amount Ellen spent. Now, we need to subtract this total from her initial amount. So, we have P700 - P570. Performing this subtraction, we find that Ellen has P130 left. This is the final step in our calculation, and it gives us the answer we were looking for.

To ensure our answer is correct, it's always a good idea to double-check our work. We can do this by adding the amount Ellen spent to the amount she has left. If P570 (total spent) + P130 (amount left) equals P700 (initial amount), then our calculation is correct. This verification step is a great way to catch any potential errors and build confidence in our solution. So, with a bit of careful calculation, we've determined that Ellen has P130 remaining after her purchases. Great job, guys!

Final Answer and Wrap-up

So, let's wrap things up and clearly state the final answer! After working through all the steps, we've determined that Ellen has P130 left after buying the cassette tape and the T-shirt. This is a concise and clear answer to the original question. When solving word problems, it's important not only to calculate the correct number but also to present the answer in a way that directly addresses the question asked.

In this case, the question was, "How much money does Ellen have left?" Our final answer, P130, directly answers this question. Additionally, it's helpful to include the unit of currency (P for Philippine Peso) to provide context and avoid any ambiguity. This attention to detail ensures that the answer is fully understood. Moreover, summarizing the process we followed can reinforce the learning. We started by understanding the problem, identified the operations needed (addition and subtraction), wrote the mathematical sentence, performed the calculations, and finally, stated the answer.

By systematically addressing each aspect of the problem, we not only arrived at the correct solution but also reinforced our problem-solving skills. Remember, guys, math problems are like puzzles, and each step we take brings us closer to completing the puzzle and finding the solution. Practice makes perfect, so keep tackling those math challenges!