Sammie's Checking Account Balance Solving For Initial Amount

In this article, we will analyze a mathematical problem involving a checking account balance. The scenario involves Sammie, who withdraws $25 from her account, leaving her with $100. Our primary goal is to determine the equation that accurately represents the situation and helps us calculate the initial amount, c, in Sammie's account before the withdrawal. We will delve into the problem-solving process, exploring different equation options, and ultimately identifying the correct equation that models the given scenario. This exercise is not only crucial for understanding basic algebraic concepts but also for developing practical problem-solving skills applicable in everyday financial situations.

The core of our problem lies in understanding the relationship between the initial amount in Sammie's account, the amount she withdrew, and the remaining balance. The problem states that Sammie took $25 out of her checking account. Following this withdrawal, she had $100 remaining. The task is to identify the equation that can be used to find the amount, c, Sammy had in her account before she took the money out. This requires us to translate the word problem into a mathematical equation, a fundamental skill in algebra. To effectively solve this, we need to consider how the withdrawal affects the account balance and how we can represent this change mathematically.

To correctly formulate the equation, let's break down the scenario step by step. Sammie starts with an unknown amount, which we denote as c. She then withdraws $25 from this amount. In mathematical terms, this withdrawal represents a subtraction operation. So, we are subtracting $25 from the initial amount c. The result of this subtraction is the remaining balance in her account, which is given as $100. Therefore, the problem can be visualized as: Initial amount (c) minus the withdrawal ($25) equals the remaining balance ($100). This clear understanding of the sequence of events and their mathematical representation is crucial for constructing the correct equation.

Now, let's consider the given equation options and evaluate which one accurately represents the scenario we've analyzed.

We need to find an equation that shows the initial amount, c, being reduced by $25 to result in $100. This process of elimination will lead us to the equation that correctly models the relationship between the initial balance, the withdrawal, and the final balance. It’s a critical step in ensuring we apply the correct mathematical operation to solve the problem.

Based on our analysis, the equation that accurately represents the scenario is:

c - 25 = 100

This equation signifies that the initial amount in Sammie's account (c), minus the $25 withdrawal, equals the remaining $100. This directly translates the problem statement into a mathematical expression. The other options presented do not logically follow the scenario. For instance, multiplying or dividing c by 25 would not reflect the act of withdrawing money, which is a subtraction operation. This equation is the cornerstone for solving the problem and determining the initial amount in Sammie's account.

To find the value of c, which represents the initial amount in Sammie's account, we need to solve the equation c - 25 = 100. This involves isolating c on one side of the equation. To do this, we perform the inverse operation of subtraction, which is addition. We add 25 to both sides of the equation to maintain the balance. This gives us:

c - 25 + 25 = 100 + 25

Simplifying this, we get:

c = 125

Therefore, the initial amount in Sammie's account before the withdrawal was $125. This step-by-step solution demonstrates the application of basic algebraic principles to solve real-world problems.

To ensure the accuracy of our solution, it's crucial to verify it against the original problem statement. We found that c = $125. Now, let's substitute this value back into the equation c - 25 = 100. Replacing c with $125, we get:

$125 - $25 = $100

This simplifies to:

$100 = $100

Since the equation holds true, our solution is correct. This verification step is a vital practice in mathematical problem-solving, as it confirms that our calculated value aligns with the conditions of the problem. It reinforces the reliability of our answer and enhances our understanding of the problem-solving process.

In conclusion, the equation that can be used to find the amount, c, Sammy had in her account before she took the money out is c - 25 = 100. By solving this equation, we determined that Sammie initially had $125 in her account. This exercise demonstrates the importance of translating real-world scenarios into mathematical equations and applying algebraic principles to solve them. The ability to formulate and solve such equations is a fundamental skill in mathematics and has practical applications in various aspects of life, particularly in financial management. Understanding these concepts empowers individuals to make informed decisions and solve problems effectively.

The problem we solved is a basic example of how algebraic equations can be used in personal finance. Similar equations can help in budgeting, calculating expenses, or determining savings goals. For instance, if you want to save a certain amount of money each month, you can use an equation to calculate how long it will take to reach your goal. Understanding these concepts is crucial for financial literacy and can aid in making sound financial decisions. To further enhance your understanding, you can explore more complex algebraic problems involving multiple variables or scenarios. This could include calculating interest on loans or investments, understanding the impact of inflation, or planning for long-term financial goals. Resources like online tutorials, educational websites, and textbooks offer a wealth of information and practice problems to deepen your knowledge and skills in this area.

The ability to translate real-world problems into mathematical equations and solve them is a valuable skill that extends beyond the classroom. It empowers us to analyze situations, make informed decisions, and solve problems effectively in various aspects of life. By understanding the fundamental principles of algebra and practicing problem-solving techniques, we can enhance our analytical abilities and apply them to everyday challenges. This exercise with Sammie's checking account balance serves as a stepping stone to more complex mathematical concepts and their practical applications. As we continue to learn and explore, we gain a deeper appreciation for the power of mathematics in understanding and navigating the world around us.