Calculate Total Expenses Correct Expression For Three Friends Spending

In this article, we will delve into a mathematical problem concerning the calculation of total expenses incurred by three friends Chris, Ben, and Danica on food and drinks. The goal is to identify the correct mathematical expression that accurately represents the total amount spent by all three friends. To address this, we will dissect the provided data, explore different mathematical approaches, and pinpoint the expression that precisely reflects the cumulative expenses. This analysis is crucial not only for solving the immediate problem but also for understanding fundamental mathematical principles related to addition and data aggregation. We will examine why certain expressions are valid while others are not, thereby enhancing your problem-solving skills and mathematical acumen. Let’s begin by thoroughly examining the expense data for each friend, setting the stage for a detailed calculation and expression analysis.

Deconstructing the Problem

Before diving into the mathematical expressions, it’s crucial to understand the core of the problem. We have three individuals Chris, Ben, and Danica each spending different amounts on food and drinks. Chris spent $5, Ben spent $3, and Danica spent $6. The question asks us to find an expression that calculates the total amount spent by all three friends combined. This is a straightforward addition problem at its heart, but the challenge lies in correctly representing this addition using a mathematical expression. The expression needs to accurately capture the sum of their individual expenses. To do this effectively, we need to ensure that we add each person's expenses only once and that no expenses are missed or double-counted. The correct expression should be clear, concise, and directly reflect the total expenditure. Understanding this foundational requirement is essential for evaluating potential expressions and determining the right answer. The following sections will explore the correct methodologies for achieving this.

Analyzing the Given Data

The data provided is straightforward and essential for solving this problem. We have a simple table that outlines the expenses of each friend. Chris spent $5, Ben spent $3, and Danica spent $6 on food and drinks. This information is the cornerstone of our calculations. To find the total amount spent, we need to sum these individual amounts. This is a basic arithmetic operation, but it’s important to ensure that the operation is represented accurately in the final expression. Each number represents a discrete amount spent by a particular person, and our goal is to combine these amounts into a single total. This step highlights the importance of clear data interpretation in mathematical problem-solving. By carefully noting each person's expenditure, we lay the groundwork for formulating and evaluating the expressions that aim to calculate the total spending. Now, let’s move on to exploring potential expressions that could correctly calculate this total.

Evaluating the Expression (3+5) × (5+3+6)

The expression presented, (3+5) × (5+3+6), requires careful evaluation to determine its validity in calculating the total expenses. Let’s break it down step by step. First, we evaluate the terms inside the parentheses. (3+5) equals 8. This part of the expression doesn't directly correlate to any specific aspect of the problem, as it seems to arbitrarily add two of the expenses. Next, we evaluate (5+3+6), which represents the sum of all individual expenses. This part correctly adds Chris's, Ben's, and Danica's expenses, resulting in 14. However, the expression then multiplies these two results, 8 and 14, which gives us 112. This multiplication does not logically follow from the problem's requirement to find the total expenses. Multiplying the sum of expenses by an arbitrary sum of two expenses does not provide a meaningful result in this context. Therefore, this expression is not suitable for finding the total amount spent by the three friends. The next section will delve into the correct approach to formulating such an expression.

Identifying the Correct Expression

To correctly find the total amount spent by Chris, Ben, and Danica, we need to formulate an expression that accurately reflects the sum of their individual expenses. The correct approach involves adding each person's spending directly together, without any extraneous operations. This means we should add Chris’s $5, Ben’s $3, and Danica’s $6. The expression that represents this operation is simply 5 + 3 + 6. This expression clearly and directly sums the expenses of each individual, providing the total amount spent. There are no additional operations that could distort the result, making this the most straightforward and accurate way to calculate the total. This method aligns perfectly with the problem's requirements, as it captures the cumulative spending without introducing unnecessary complexity. Understanding this direct approach is crucial for solving similar problems involving the summation of individual values. In the following sections, we will further discuss why this expression is correct and how it contrasts with the incorrect expression we previously analyzed.

The Correct Calculation: 5 + 3 + 6

The expression 5 + 3 + 6 is the accurate representation of the total expenses incurred by Chris, Ben, and Danica. Let's calculate the result. Adding the numbers sequentially, 5 plus 3 equals 8, and then adding 6 to 8 gives us 14. Therefore, the total amount spent by all three friends is $14. This calculation is straightforward and aligns directly with the problem's requirement to find the combined expenses. Each number represents an individual's spending, and the addition operation correctly aggregates these amounts. There are no hidden complexities or unnecessary operations; the expression simply sums the given values. This clarity is essential in mathematical problem-solving, as it ensures that the solution is both accurate and easily understandable. This result provides a clear answer to the problem, showcasing the simplicity and effectiveness of direct addition in calculating totals. The next section will summarize the key points and reinforce the methodology used to arrive at this conclusion.

Conclusion: Summing Up the Total Expenses

In conclusion, the problem required us to determine the total amount spent by Chris, Ben, and Danica on food and drinks. By carefully analyzing the data, we identified that Chris spent $5, Ben spent $3, and Danica spent $6. The correct approach to finding the total expenses involved summing these individual amounts. The expression 5 + 3 + 6 accurately represents this sum, resulting in a total of $14. We also examined the incorrect expression (3+5) × (5+3+6), which involved multiplying a partial sum by the total sum, leading to an inaccurate result. Understanding why the direct addition method is correct is crucial for solving similar problems. This exercise underscores the importance of interpreting data accurately, selecting appropriate mathematical operations, and avoiding unnecessary complexity. The direct summation method provides a clear and efficient way to calculate totals, ensuring accurate and understandable results. This comprehensive analysis equips you with the skills to tackle similar problems confidently and effectively.

Which expression accurately calculates the total amount of money spent by Chris, Ben, and Danica on tickets, food, and drinks, given their individual expenses?

Calculate Total Expenses Correct Expression for Three Friends Spending