Sammie's Checking Account Balance Finding The Initial Amount

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Hey guys! Let's dive into a math problem that involves figuring out how much money Sammie had in her checking account before she made a withdrawal. This is a classic example of how we can use equations to represent real-life situations. So, grab your thinking caps, and let's break it down!

Understanding the Problem

So, here's the deal: Sammie, our main character for today, withdrew 25 dollars from her checking account. After this transaction, she checked her balance and found a cool 100 dollars sitting there. The question we need to answer is: How much money, represented by the variable c, did Sammie have in her account before she took out the 25 bucks? This problem is a perfect example of how we can use algebraic equations to solve everyday financial scenarios. We need to figure out the initial amount, the starting point, before the withdrawal happened. Think of it like retracing Sammie's steps – we know where she ended up, and we need to figure out where she began.

To really grasp what's going on, let's visualize the situation. Imagine a number line, or even just a mental image of a bank statement. Sammie started with some amount, c. Then, a withdrawal of $25 happened, which means we're subtracting $25 from her initial amount. This subtraction leads us to the final balance of $100. Our goal is to find that initial amount, c. We need an equation that accurately reflects this scenario, an equation that shows the relationship between the starting amount, the withdrawal, and the final balance. This is where our understanding of basic algebra comes into play. We'll need to translate the words of the problem into a mathematical statement, a concise equation that captures the essence of Sammie's financial situation. Think carefully about how addition and subtraction play a role here. Are we adding the withdrawal amount to the final balance, or are we subtracting it? The correct choice will lead us to the equation that solves the mystery of Sammie's initial balance.

Identifying the Correct Equation

Okay, so we've got four potential equations to choose from, and only one will lead us to the right answer. Let's look at each option and see which one accurately represents the situation:

  • A. c × 25 = 100 This equation suggests that Sammie's initial amount multiplied by 25 equals 100. Does that make sense in our scenario? No, not really. We know Sammie subtracted money, not multiplied it. So, we can eliminate this option.

  • B. c ÷ 25 = 100 This one says Sammie's initial amount divided by 25 equals 100. Again, this doesn't fit our problem. Division isn't the operation we need here, since money was taken out of the account.

  • C. c - 25 = 100 Now we're talking! This equation states that Sammie's initial amount minus 25 dollars equals 100 dollars. This perfectly aligns with the problem description. We started with an unknown amount, took away 25, and ended up with 100. This is a strong contender.

  • D. c + 25 = 100 This option says Sammie's initial amount plus 25 dollars equals 100 dollars. This is the opposite of what happened. We need to account for the fact that Sammie withdrew money, which means subtraction, not addition.

So, after analyzing each option, it's clear that C. c - 25 = 100 is the equation that correctly models the situation. It shows that the initial amount, c, decreased by $25, resulted in the final balance of $100. This equation is the key to unlocking the mystery of Sammie's starting balance.

Solving the Equation

Alright, we've identified the correct equation: c - 25 = 100. Now, let's actually solve it to find out exactly how much money Sammie had in her account before her withdrawal. This is where our algebra skills really shine. We need to isolate c on one side of the equation, which means getting rid of that pesky -25. To do that, we use the inverse operation. Since we're subtracting 25, the inverse operation is adding 25. Remember, whatever we do to one side of the equation, we must do to the other side to keep things balanced.

So, here's how we solve it:

  • Start with the equation: c - 25 = 100
  • Add 25 to both sides: (c - 25) + 25 = 100 + 25
  • Simplify: c = 125

There you have it! We've solved for c, and we found that Sammie had 125 dollars in her account before she took out the 25 bucks. This is a fantastic example of how algebraic equations can help us solve real-world problems. By understanding the relationship between the initial amount, the withdrawal, and the final balance, we were able to construct an equation and use inverse operations to find the solution. This process of translating a word problem into a mathematical equation and then solving it is a fundamental skill in algebra, and it's something that you'll use again and again in various contexts.

Conclusion

So, to wrap it all up, the equation that can be used to find the amount, c, Sammie had in her account before she took the money out is c - 25 = 100. And by solving this equation, we discovered that Sammie initially had $125 in her checking account. This problem highlights the power of algebra in representing and solving real-life financial scenarios. Keep practicing these types of problems, and you'll become a math whiz in no time! Remember, the key is to carefully read the problem, identify the relationships between the quantities involved, and translate those relationships into a mathematical equation. Once you have the equation, solving it is often just a matter of applying the appropriate algebraic techniques, like using inverse operations to isolate the variable. So, keep those thinking caps on, and keep exploring the fascinating world of mathematics!