Calculating Bank Account Balance After Weekly Withdrawals

Hey guys! Let's dive into a fun math problem that many of us can relate to – managing our bank accounts. Imagine you're diligently writing a check for $50 every single week. That’s a consistent outflow, right? Now, let's say you're not making any new deposits during this time. The question we're tackling today is: How will your bank account balance change over a certain number of weeks? Specifically, we want to figure out what your account will hold \\$x\ weeks from now. This kind of problem is super practical because it helps us understand how recurring expenses impact our finances over time. To get started, let's break down the components we need to consider.

Understanding the Initial Balance

First off, we need to know where we're starting. Think of it like this: if you're planning a road trip, you need to know your starting point to calculate how far you'll travel. In our case, the initial balance in the bank account acts as our starting point. The problem mentions an initial amount of $500. So, this is the money we have in the account before any checks are written. This ${$500\}$ is our foundation, the amount from which we will subtract our weekly expenses. It’s crucial to identify this initial amount because it’s the anchor for all our calculations. Without knowing this, we’d be sailing in the dark, unable to predict our financial position accurately. Now, let’s hold that thought and move on to the next crucial piece of information: the weekly check amount. Imagine this ${$500\}$ as a pie, and each week, we're slicing off a piece to pay our expenses. The size of that piece is determined by the weekly check amount, which we'll explore in the next section.

Calculating Weekly Expenses

Next up, let’s zoom in on those weekly expenses. The problem clearly states that a check for $50 is written each week. This ${$50\}$ represents a consistent, recurring expense. It’s like a subscription fee or a regular bill that you pay without fail every week. Now, here's where things get interesting. We need to figure out how this weekly expense impacts our total balance over time. Each week, the ${$50\}$ is subtracted from our initial balance. This is a crucial step in understanding the overall change in the account. To visualize this, imagine you’re filling a glass of water, but at the same time, there’s a small hole at the bottom, slowly draining the water out. The ${$50\}$ weekly expense is like that hole, constantly reducing the amount of money in your account. So, how do we quantify this over multiple weeks? That’s where the variable ${x}$ comes into play. The variable ${x}$ represents the number of weeks we’re considering. If we want to know the total expense over ${x}$ weeks, we simply multiply the weekly expense by the number of weeks. This gives us a total expense of ${50x}$ dollars. Now, let’s pause here and make sure we’re all on the same page. We started with an initial balance of ${$500\}$, and over ${x}$ weeks, we’ve accumulated a total expense of ${$50x\}$. The next step is to combine these two pieces of information to find the final balance in the account. Think of it as putting the pieces of a puzzle together – we have the initial amount and the total expense, and now we need to see how they fit together.

Determining the Final Balance

Alright, guys, let's put it all together and figure out the final balance in the account. We started with that sweet ${$500\}$, and we know that each week, ${$50\}$ is going out the door. We've also established that over ${x}$ weeks, the total expense is ${$50x\}$. So, how do we find out what's left in the account after ${x}$ weeks? It’s actually pretty straightforward: we subtract the total expenses from the initial balance. This gives us the equation: Final Balance = Initial Balance – Total Expenses. Plugging in our values, we get: Final Balance = ${$500 – $50x\}$. This equation tells us exactly how the balance changes over time. The ${$500\}$ is our starting point, and the ${- $50x\}$ represents the decrease in the balance due to the weekly checks. For example, if we want to know the balance after 1 week, we substitute ${x}$ with 1: Final Balance = ${$500 – $50(1) = $450\}$. After 2 weeks: Final Balance = ${$500 – $50(2) = $400\}$. See how it works? Each week, the balance decreases by ${$50\}$. This equation is a powerful tool because it allows us to predict the balance at any point in the future, as long as we know the number of weeks. Now, let's take a step back and look at the answer choices provided in the problem. We need to identify which option matches our equation. Remember, we're looking for an expression that represents the final balance after ${x}$ weeks. The correct answer should reflect the initial balance of ${$500\}$ and the weekly deduction of ${$50\}$. Let’s review the options.

Evaluating the Answer Choices

Okay, let's put on our detective hats and carefully examine the answer choices provided. Our mission? To find the expression that perfectly matches our calculated final balance: ${$500 – $50x\}$. Let's break down each option and see how it stacks up.

• Option A: ${$500 + $50x\}$ This option represents an increase in the balance over time. Instead of subtracting the weekly expense, it adds it. This would mean the account is growing by ${$50\}$ each week, which is the opposite of what's happening in our scenario. So, Option A is definitely not the correct answer.
• Option B: ${$500 – $50x\}$ Aha! This looks promising. This option subtracts ${$50x\}$ from the initial ${$500\}$, which is exactly what we need. The ${$50x\}$ represents the total expenses over ${x}$ weeks, and we're subtracting it from the starting balance. This aligns perfectly with our equation and our understanding of the problem. So, Option B is a strong contender.
• Option C: ${$550 – x\}$ This option is a bit of a tricky one. It subtracts ${x}$ from ${$550\}$, but it doesn't account for the ${$50\}$ weekly expense. It's as if we're subtracting ${$1\}$ for each week, which doesn't match our scenario. The weekly expense is ${$50\}$, not ${$1\}$, so this option is incorrect.
• Option D: ${$500 + $50 + x\}$ This option is a bit of a mishmash. It adds ${$50\}$ to the initial ${$500\}$, which is unnecessary, and then adds ${x}$, which doesn't make sense in the context of our problem. It's not clear what this expression is trying to represent, and it certainly doesn't match our calculated final balance. So, Option D is also incorrect.

After carefully evaluating each option, it's clear that Option B (${$500 – $50x\}$) is the winner. It perfectly represents the final balance in the account after ${x}$ weeks, taking into account the initial balance and the weekly expenses. So, we've cracked the code! We've not only found the correct answer but also understood the reasoning behind it. That’s the real victory, guys! Understanding the ‘why’ behind the math makes it so much more powerful and useful in real-life situations.

Final Answer

So, after walking through the problem step by step, from understanding the initial balance to calculating weekly expenses and finally determining the final balance, we've arrived at our answer. We carefully evaluated each option and found that Option B, which is ${$500 – $50x\}$, perfectly represents the balance in the bank account after ${x}$ weeks. This equation takes into account the initial ${$500\}$ and subtracts the total expenses of ${$50x\}$, giving us a clear picture of how the balance changes over time. This type of problem is a fantastic way to sharpen our financial literacy skills. It’s not just about crunching numbers; it’s about understanding how our spending habits impact our bank accounts and our overall financial health. By breaking down the problem into smaller, manageable parts, we were able to tackle it with confidence and clarity. And that, my friends, is the power of math! It’s not just about getting the right answer; it’s about building a solid understanding that we can apply to real-world situations. So, keep practicing, keep exploring, and keep those financial wheels turning!