Hey guys! Ever find yourself trying to backtrack a transaction to figure out where you started? Today, we’re diving into a classic math problem that’s super relatable. We’re going to help Sammie figure out her initial checking account balance using a simple equation. So, grab your thinking caps, and let’s get started!
Understanding the Problem
Before we jump into solving equations, let’s break down the problem. Sammie withdrew $25 from her checking account. This means she took $25 out, reducing her balance. After this withdrawal, she had $100 left. The big question is: How much money did Sammie have in her account before she took out the $25? To solve this, we need to set up an equation that represents this scenario. Think of it like retracing Sammie’s steps but in reverse! We need to consider that the $100 is what’s left after the $25 was taken out, so we need to figure out what the original amount was. This is a common type of problem in basic algebra, and mastering it can help you in many real-life situations, from balancing your checkbook to understanding financial transactions. Remember, math isn't just about numbers; it's about problem-solving and logical thinking. By understanding the problem thoroughly, we can create a solid plan to find the solution. Let's move on to how we can formulate an equation to represent Sammie's situation accurately.
Formulating the Equation
Okay, so now we know what we need to find: Sammie's initial amount. In algebra, we often use a variable to represent an unknown value. In this case, let’s use the variable “c” to stand for the amount Sammie had in her account before the withdrawal. Now, let's think about what happened. Sammie took out $25, which means we’re subtracting $25 from her initial amount. After this subtraction, she had $100 left. So, we can express this situation as an equation. The equation should show that the initial amount c, minus the $25 withdrawal, equals the remaining $100. This can be written as: c - 25 = 100. This equation is the key to solving our problem. It tells us exactly how the different amounts relate to each other. By setting up the equation correctly, we’ve translated the word problem into a mathematical statement that we can solve. It’s like having a roadmap that guides us to the answer! In this equation, c is our starting point, the $25 is the step we take backward (the withdrawal), and $100 is where we end up. The equation clearly shows the relationship between these values, making it easier to find the missing piece – Sammie’s initial balance. Now that we have our equation, let's explore how to solve it.
Solving the Equation
Alright, we’ve got our equation: c - 25 = 100. The goal here is to isolate “c” on one side of the equation. This means we want to get “c” all by itself, so we know exactly what it equals. To do this, we need to reverse the operation that’s being done to “c”. In this case, we’re subtracting 25 from “c”. The opposite of subtraction is addition, so we need to add 25 to both sides of the equation. Why both sides? Because in an equation, whatever you do to one side, you have to do to the other to keep the equation balanced. It’s like a seesaw – if you add weight to one side, you need to add the same weight to the other side to keep it level. So, let's add 25 to both sides of our equation: c - 25 + 25 = 100 + 25. On the left side, the -25 and +25 cancel each other out, leaving us with just “c”. On the right side, 100 + 25 equals 125. So, our equation simplifies to c = 125. This means that Sammie had $125 in her account before she took out the $25. See how we used the inverse operation to get “c” by itself? That’s a fundamental concept in algebra. By understanding how to manipulate equations, you can solve all sorts of problems. Now, let's make sure we've got the right answer by checking our work.
Verifying the Solution
Okay, we’ve found that c = 125, which means we think Sammie started with $125 in her account. But before we celebrate, it’s super important to check our answer. This is a crucial step in problem-solving because it ensures we haven’t made any mistakes along the way. To verify our solution, we’re going to plug the value we found for “c” back into our original equation: c - 25 = 100. So, we replace “c” with 125: 125 - 25 = 100. Now, let’s simplify the left side of the equation. 125 minus 25 equals 100. So, we have 100 = 100. This is a true statement! It means that our solution is correct. When both sides of the equation are equal after substituting the value of the variable, it confirms that we’ve found the correct answer. Checking your work might seem like an extra step, but it’s a lifesaver. It helps you catch any errors and gives you confidence in your solution. In this case, we’ve verified that Sammie indeed had $125 in her account before withdrawing $25. Pat yourself on the back – you’ve solved the problem! Now, let's reflect on what we’ve learned and how we approached this problem.
Conclusion
So, we’ve successfully helped Sammie figure out her initial checking account balance! We started by understanding the problem, then we translated it into an algebraic equation, solved the equation using inverse operations, and finally, we verified our solution. This step-by-step approach is a powerful tool for tackling all sorts of math problems. Remember, the key to solving word problems is to break them down into smaller, manageable parts. Identify the unknown, represent it with a variable, and then write an equation that shows the relationship between the different values. Don't forget to check your work – it's the best way to ensure accuracy. This problem is a great example of how math concepts can be applied to everyday situations. Whether you're managing your finances, planning a budget, or just trying to figure out how much money you had before that impulse purchase, understanding basic algebra can be incredibly helpful. Keep practicing, and you’ll become a math whiz in no time! And remember, math isn't just about getting the right answer; it's about the process of problem-solving and the logical thinking skills you develop along the way. So, the next time you encounter a similar problem, you’ll be ready to tackle it with confidence. Great job, guys, on solving this problem with Sammie!
