Calculating Gym Membership Costs Total For 12 Classes

This article delves into a practical mathematical problem involving gym membership costs and class fees. We'll explore how to calculate the total amount Harry has to pay for his gym membership, considering both the fixed monthly fee and the per-class charges. This is a common scenario that many individuals encounter when joining a gym or fitness center, making it a relatable and useful example for understanding linear equations and cost calculations. We will break down the problem step-by-step, providing a clear explanation of the formula used and how to apply it. Whether you're a student learning about algebraic equations or someone trying to budget for fitness expenses, this article will offer valuable insights.

Understanding the Problem A Breakdown of Gym Membership Fees

At the heart of our problem is the need to determine the total cost Harry incurs for his gym usage. This cost is composed of two parts a fixed monthly membership fee and a variable cost dependent on the number of classes he attends. Harry's situation is a perfect example of a linear equation in action, where the total cost is a function of the number of classes attended. The fixed monthly fee acts as the y-intercept, the starting point regardless of class attendance. The per-class fee represents the slope, the rate at which the total cost increases with each additional class. Understanding these components is crucial for accurately calculating the total cost. In this case, Harry pays a flat $28 for his one-month gym membership. This is a fixed cost, meaning it remains the same regardless of how many classes he attends. In addition to the membership fee, Harry has to pay $2 for every class he takes. This is a variable cost, as it depends on the number of classes, represented by x. Therefore, if Harry takes more classes, his total cost will increase, and if he takes fewer classes, his total cost will decrease. This variable cost is a crucial element in determining the overall expense of Harry's gym membership.

The Formula for Total Cost: f(x) = 2x + 28

The provided formula, f(x) = 2x + 28, is a mathematical expression that encapsulates the total amount Harry has to pay. Let's dissect this formula to understand its components and how they relate to the problem. This formula is a linear equation, a fundamental concept in algebra. Linear equations are used to model relationships where the change in one variable is directly proportional to the change in another. In our context, the total cost, f(x), changes linearly with the number of classes, x, Harry attends. The formula’s structure follows the slope-intercept form of a linear equation, y = mx + b, where m represents the slope and b represents the y-intercept. Here, f(x) represents the total cost, which is the dependent variable, while x represents the number of classes, the independent variable. The coefficient 2 in front of x represents the cost per class. This means that for every class Harry takes, he pays an additional $2. This is the slope of the linear equation, indicating the rate of change in the total cost with respect to the number of classes. The constant 28 represents the one-month gym membership fee. This is a fixed cost that Harry has to pay regardless of how many classes he attends. In the context of the linear equation, this is the y-intercept, the value of f(x) when x is zero. This component ensures that even if Harry doesn't attend any classes, he still incurs the $28 membership fee. By using this formula, we can easily calculate the total cost for any given number of classes. Simply substitute the number of classes for x and perform the calculation. This formula is a powerful tool for understanding and predicting Harry's gym expenses.

Calculating the Total Cost for 12 Classes: A Step-by-Step Solution

Now, let's apply the formula to determine the total amount Harry has to pay if he takes 12 classes. This involves substituting the value of x (the number of classes) into the equation and performing the arithmetic operations. This process demonstrates how algebraic equations can be used to solve real-world problems involving cost calculations and budgeting. The problem states that Harry takes 12 classes, so we substitute x with 12 in the formula: f(x) = 2x + 28 becomes f(12) = 2(12) + 28. The next step is to perform the multiplication. We multiply 2 by 12, which equals 24. So, the equation now looks like this: f(12) = 24 + 28. Finally, we add 24 and 28 together. 24 plus 28 equals 52. Therefore, f(12) = 52. This result signifies that the total amount Harry has to pay if he takes 12 classes is $52. This calculation combines the variable cost of the classes ($24 for 12 classes) with the fixed monthly membership fee ($28), providing a comprehensive understanding of his expenses. This example clearly illustrates the application of linear equations in managing personal finances and making informed decisions about gym memberships and class attendance.

The Answer and Its Implications: Harry's Total Gym Expenses

Based on our calculations, the total amount Harry has to pay if he takes 12 classes is $52. This corresponds to option A in the given choices. This answer highlights the importance of understanding the interplay between fixed and variable costs when budgeting for expenses like gym memberships. It also showcases how mathematical formulas can provide a clear and precise way to calculate total costs and make informed financial decisions. The $52 total cost comprises the fixed monthly membership fee of $28 and the variable cost of $2 per class for 12 classes, totaling $24. This breakdown allows Harry to see exactly how much he's spending on each aspect of his gym membership. Understanding these costs can help Harry make decisions about his gym usage. For example, if he finds the total cost too high, he might consider attending fewer classes or exploring alternative gym options with different pricing structures. This calculation is not just about finding the right answer; it's about empowering Harry (and anyone facing similar financial decisions) to understand and manage their expenses effectively. The use of the formula f(x) = 2x + 28 provides a clear and consistent method for calculating these costs, making it easier to plan and budget for fitness activities. This practical application of mathematics demonstrates its relevance in everyday life and financial planning.

Conclusion: The Power of Math in Everyday Budgeting

In conclusion, by applying the formula f(x) = 2x + 28, we were able to accurately calculate that Harry has to pay $52 if he takes 12 classes. This exercise demonstrates the practical application of mathematical concepts, specifically linear equations, in real-world scenarios such as budgeting and expense management. The problem highlights the importance of understanding both fixed costs (the monthly membership fee) and variable costs (the per-class fee) when planning for expenses. This understanding allows individuals to make informed decisions about their spending and optimize their budget. Furthermore, this example showcases the power of mathematical formulas in providing a clear and concise method for calculating total costs. By substituting the number of classes into the formula, we can quickly determine the total expense, making it easier to plan and budget for gym memberships and other activities with similar cost structures. This ability to calculate and predict expenses is a valuable skill in personal finance, enabling individuals to make responsible financial choices. Ultimately, this problem serves as a reminder that mathematics is not just an abstract subject taught in classrooms; it is a powerful tool that can be applied to solve everyday problems and improve financial literacy.

Answer: A. $52