What Equation Represents The Total Price (p) When Buying Books (b) At $3.99 Each, And How Much Will 13 Books Cost?

In the realm of everyday mathematics, understanding how to calculate the total cost of multiple items is a fundamental skill. This article delves into a specific scenario: determining the total price (p) of buying books (b) when each book costs $3.99. We'll explore how to represent this situation using an equation and then apply the equation to find the cost of purchasing 13 books. Understanding this concept is crucial for budgeting, financial planning, and making informed purchasing decisions. Let's begin by constructing the equation that accurately models the relationship between the number of books bought and the total price paid.

Formulating the Equation: Linking Books and Price

At the heart of this problem lies the relationship between the number of books purchased and the total cost incurred. Each book has a fixed price of $3.99, so the total price will directly depend on how many books you buy. To express this relationship mathematically, we need to formulate an equation. This equation will serve as a tool to calculate the total cost for any number of books. The core concept here is that the total price (p) is equal to the price per book ($3.99) multiplied by the number of books (b). We can express this mathematically as p = 3.99 * b. This equation is the cornerstone of our calculations. It clearly demonstrates how the total price varies with the number of books purchased. It's a linear equation, meaning that the relationship between the number of books and the total price can be represented by a straight line on a graph. This simplicity makes it a powerful tool for quick and easy calculations. The equation also highlights the direct proportionality between the number of books and the total price. As you increase the number of books, the total price increases proportionally, and vice versa. The constant of proportionality here is $3.99, which is the price per book. This equation is not just a mathematical formula; it's a representation of a real-world scenario. It allows us to predict the total cost before we even make a purchase, enabling us to budget effectively. It also helps us understand the underlying relationship between quantity and price, a concept that is fundamental to economics and business. The equation p = 3.99 * b is more than just a formula; it's a tool for understanding and managing our finances. Now that we have our equation, let's put it to work and calculate the cost of buying 13 books. This will demonstrate the practical application of our equation and further solidify our understanding of the relationship between books and price. Understanding and applying this equation lays a solid foundation for tackling more complex financial calculations in the future.

Calculating the Cost of 13 Books: Putting the Equation to Work

Now that we have our equation, p = 3.99b, we can use it to calculate the total cost of purchasing 13 books. This step involves substituting the value of b (the number of books) with 13 and then performing the multiplication. This is a straightforward application of the equation and will give us a concrete answer to the question of how much 13 books will cost. The substitution process is a fundamental concept in algebra. It allows us to take a general equation and apply it to specific situations. In this case, we are taking the general equation that relates the total price to the number of books and applying it to the specific situation where we want to buy 13 books. The calculation itself is simple multiplication: 3.99 multiplied by 13. This can be done manually, using a calculator, or even with a spreadsheet program. The result of this calculation will be the total cost in dollars. It's important to remember the units when working with mathematical equations. In this case, the price per book is in dollars, and the number of books is a unitless quantity. Therefore, the total price will also be in dollars. This consistency of units is crucial for accurate calculations and interpretations. Once we have the total cost, we can then use this information for budgeting or decision-making purposes. For example, if we have a budget of $50, we can see that 13 books will exceed our budget. This simple calculation can help us make informed choices about our purchases. The process of calculating the cost of 13 books is not just about finding a numerical answer. It's about applying our understanding of the equation and the relationship it represents to a real-world scenario. It's about taking a mathematical concept and using it to solve a practical problem. This is the essence of mathematical literacy – the ability to understand and apply mathematical concepts in everyday life. By working through this calculation, we are not just finding the cost of 13 books; we are also strengthening our understanding of mathematical principles and their applications. Let's proceed with the calculation and find out exactly how much 13 books will cost at $3.99 each. This will provide a tangible example of how the equation works and how it can be used in practical situations.

Step-by-Step Calculation: Finding the Total Price

To determine the total cost of 13 books at $3.99 each, we'll perform a straightforward multiplication using the equation p = 3.99b. As we established, p represents the total price, and b represents the number of books. In this scenario, b is 13, so we will substitute 13 for b in the equation. This step-by-step approach will ensure clarity and accuracy in our calculation. First, we write down the equation: p = 3.99 * b. Next, we substitute the value of b: p = 3.99 * 13. Now, we perform the multiplication. This can be done using a calculator or by hand. Multiplying 3.99 by 13 gives us 51.87. Therefore, p = 51.87. This means that the total price of 13 books is $51.87. This result is a concrete answer to our initial question. It tells us exactly how much it will cost to purchase 13 books at the given price. The calculation highlights the importance of accurate arithmetic. Even a small error in the multiplication can lead to a significant difference in the total price. This is why it's always a good idea to double-check your calculations, especially when dealing with financial matters. The result also reinforces our understanding of the equation. It shows us how the equation can be used to predict the total cost for any number of books. By substituting different values for b, we can easily calculate the total price for any quantity of books. This makes the equation a versatile tool for budgeting and financial planning. The step-by-step calculation also illustrates the power of mathematical notation. The equation p = 3.99 * 13 concisely represents the entire calculation process. It allows us to express the relationship between the number of books and the total price in a clear and unambiguous way. Now that we have calculated the total cost, we can confidently say that 13 books at $3.99 each will cost $51.87. This is a practical example of how mathematical equations can be used to solve real-world problems.

Identifying the Correct Option: Matching the Equation and the Total Price

Having derived the equation p = 3.99b and calculated the total cost of 13 books as $51.87, we can now confidently identify the correct answer choice from the given options. This step involves comparing our results with the options provided and selecting the one that matches both the equation and the total price. This is a crucial step in problem-solving, as it ensures that we not only understand the underlying concepts but also can apply them to select the correct solution from a set of possibilities. The process of elimination can be a helpful strategy here. We can first look for the option that correctly represents the equation relating the total price and the number of books. Then, we can verify that the calculated total price for 13 books matches the price given in the option. This systematic approach helps to avoid errors and ensures that we select the most accurate answer. It also reinforces our understanding of the problem and the solution process. By carefully comparing our results with the options, we are solidifying our comprehension of the mathematical concepts involved. This is an important skill not only in mathematics but also in various other fields where problem-solving is essential. The correct option will be the one that accurately represents the relationship between the total price and the number of books and provides the correct total price for 13 books. This step is not just about finding the right answer; it's about demonstrating our ability to apply our knowledge and skills to solve a problem completely. Let's carefully examine the options and identify the one that matches our findings. This will be the final step in solving this problem and will showcase our understanding of the concepts and calculations involved.

Conclusion: Understanding the Power of Equations in Everyday Calculations

In conclusion, we have successfully determined that the equation p = 3.99b represents the total price (p) paid when buying books (b) at $3.99 each, and we have calculated that 13 books would cost $51.87. This exercise highlights the power of mathematical equations in representing real-world scenarios and facilitating practical calculations. We've seen how a simple equation can be used to model the relationship between the number of items purchased and the total cost, and how this equation can be applied to calculate the cost for any given quantity. This understanding is crucial for budgeting, financial planning, and making informed purchasing decisions. The ability to formulate and use equations is a fundamental skill in mathematics and has wide-ranging applications in various aspects of life. From calculating grocery bills to planning large-scale projects, equations provide a framework for understanding and managing quantitative relationships. This problem also demonstrates the importance of accurate calculations. A small error in the multiplication could have led to an incorrect total price, highlighting the need for careful attention to detail when working with numbers. The process of solving this problem involved several key steps: formulating the equation, substituting values, performing calculations, and interpreting the results. Each of these steps is essential for effective problem-solving in mathematics. By mastering these steps, we can confidently tackle a wide range of mathematical challenges. The equation p = 3.99b is a simple example, but it illustrates the core principles of mathematical modeling. By understanding these principles, we can apply them to more complex situations and develop sophisticated models for understanding and predicting real-world phenomena. Mathematics is not just about abstract concepts; it's a powerful tool for solving practical problems and making informed decisions. This exercise has provided a concrete example of how mathematical equations can be used in everyday life. By mastering these skills, we can become more confident and effective in our personal and professional lives.