How Much Money Did Brent And Julia Earn Altogether In The Sale Of Tickets, Given That A Raffle Ticket Costs $5.00, Brent Sold 165 Tickets, And Julia Sold 3/5 Of Brent's Amount?

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Introduction

In this article, we will delve into a practical mathematics problem involving the calculation of earnings from raffle ticket sales. Understanding how to solve such problems is crucial for developing essential mathematical skills applicable in various real-life scenarios. This problem specifically focuses on multiplication, fractions, and addition, providing a comprehensive exercise in basic arithmetic operations. To truly master mathematical concepts, it is essential to break down the problem into smaller, manageable parts, identify the key information, and apply the appropriate formulas or operations. This step-by-step approach not only helps in arriving at the correct answer but also enhances problem-solving abilities, making it easier to tackle more complex mathematical challenges in the future. By understanding these fundamental principles, individuals can gain confidence in their mathematical abilities and apply them effectively in both academic and everyday situations. Furthermore, this type of problem reinforces the importance of attention to detail and the ability to interpret information accurately, skills that are valuable in a wide range of contexts.

Problem Statement

The core of our discussion revolves around a scenario where raffle tickets are sold to raise money. The problem states that each raffle ticket costs $5.00. Brent, one of the sellers, managed to sell 165 tickets. Julia, another seller, sold a fraction of the tickets Brent sold, specifically 3/5 of Brent's total. The primary objective is to determine the total amount of money Brent and Julia earned together from their ticket sales. To effectively solve this problem, we need to carefully analyze the given information and devise a step-by-step plan. The first step involves calculating the amount earned by Brent, which can be done by multiplying the number of tickets he sold by the price of each ticket. Next, we need to calculate the number of tickets Julia sold, which involves finding 3/5 of Brent's total tickets. Once we have the number of tickets Julia sold, we can calculate her earnings by multiplying this number by the price of each ticket. Finally, to find the total earnings of both Brent and Julia, we simply add their individual earnings together. This systematic approach ensures that we address each aspect of the problem and arrive at the correct solution. By breaking down the problem into smaller, more manageable steps, we can avoid confusion and minimize the chances of making errors. This method also allows us to gain a deeper understanding of the underlying mathematical concepts involved, which is essential for tackling more complex problems in the future. In essence, the key to solving this type of problem lies in careful reading, accurate interpretation, and methodical application of arithmetic operations.

Step-by-Step Solution

1. Calculate Brent's earnings

To determine how much money Brent earned, we need to multiply the number of tickets he sold by the price of each ticket. Brent sold 165 tickets, and each ticket costs $5.00. Therefore, Brent's earnings can be calculated as follows:

  • Brent's earnings = Number of tickets sold by Brent × Price per ticket
  • Brent's earnings = 165 tickets × $5.00/ticket
  • Brent's earnings = $825.00

This calculation demonstrates a fundamental principle of multiplication, where we are essentially adding the price of each ticket 165 times. The result, $825.00, represents the total amount of money Brent collected from his ticket sales. This step is crucial as it provides the first piece of the puzzle in determining the overall earnings. It's important to note the units in this calculation; we are multiplying tickets by dollars per ticket, which results in a dollar amount. This attention to units is a key aspect of mathematical problem-solving, as it ensures that the answer is not only numerically correct but also makes sense in the context of the problem. Furthermore, this calculation reinforces the concept of proportionality, where the total earnings increase linearly with the number of tickets sold. Understanding this relationship is essential for grasping more advanced mathematical concepts in the future. By carefully performing this multiplication and understanding its underlying principles, we lay a solid foundation for the subsequent steps in solving the problem.

2. Calculate the number of tickets Julia sold

To find out how many tickets Julia sold, we need to calculate 3/5 of the number of tickets Brent sold. Brent sold 165 tickets, so we need to find 3/5 of 165. This can be calculated as follows:

  • Number of tickets sold by Julia = (3/5) × Number of tickets sold by Brent
  • Number of tickets sold by Julia = (3/5) × 165 tickets
  • Number of tickets sold by Julia = (3 × 165) / 5
  • Number of tickets sold by Julia = 495 / 5
  • Number of tickets sold by Julia = 99 tickets

This calculation involves understanding the concept of fractions and how to apply them to real-world scenarios. The fraction 3/5 represents a part of a whole, in this case, a part of the total number of tickets Brent sold. To find 3/5 of 165, we multiply the numerator (3) by 165 and then divide the result by the denominator (5). This process essentially divides 165 into 5 equal parts and then takes 3 of those parts. The result, 99 tickets, represents the number of tickets Julia sold. This step is crucial because it provides the necessary information to calculate Julia's earnings. Understanding how to work with fractions is a fundamental skill in mathematics, and this problem provides a practical application of this concept. Furthermore, this calculation reinforces the idea that fractions are not just abstract numbers but can represent tangible quantities in real-life situations. By carefully performing this calculation and understanding the underlying principles of fractions, we can confidently move on to the next step in solving the problem.

3. Calculate Julia's earnings

Now that we know Julia sold 99 tickets, we can calculate her earnings by multiplying the number of tickets she sold by the price of each ticket. Each ticket costs $5.00, so Julia's earnings can be calculated as follows:

  • Julia's earnings = Number of tickets sold by Julia × Price per ticket
  • Julia's earnings = 99 tickets × $5.00/ticket
  • Julia's earnings = $495.00

This calculation is similar to the one we performed for Brent's earnings, and it reinforces the concept of multiplication as repeated addition. We are essentially adding the price of each ticket 99 times to find the total amount of money Julia collected. The result, $495.00, represents Julia's total earnings from her ticket sales. This step is crucial because it provides the second piece of the puzzle in determining the overall earnings of both Brent and Julia. It's important to note that the units in this calculation are consistent with the previous one; we are multiplying tickets by dollars per ticket, which results in a dollar amount. This consistency in units is essential for ensuring the accuracy of the final answer. Furthermore, this calculation highlights the importance of using previously calculated values (in this case, the number of tickets Julia sold) to solve subsequent parts of the problem. By carefully performing this multiplication and understanding its underlying principles, we can confidently move on to the final step in solving the problem.

4. Calculate the total earnings

To find the total amount of money Brent and Julia earned together, we need to add their individual earnings. Brent earned $825.00, and Julia earned $495.00. Therefore, the total earnings can be calculated as follows:

  • Total earnings = Brent's earnings + Julia's earnings
  • Total earnings = $825.00 + $495.00
  • Total earnings = $1320.00

This calculation involves a simple addition operation, where we are combining two amounts to find the total. The result, $1320.00, represents the total amount of money earned by Brent and Julia together from their ticket sales. This is the final answer to the problem, and it provides a comprehensive solution to the initial question. This step is crucial because it demonstrates the importance of synthesizing information from different parts of the problem to arrive at a complete solution. It also reinforces the concept of addition as a way to combine quantities. Furthermore, this calculation highlights the importance of double-checking the answer to ensure that it makes sense in the context of the problem. In this case, the total earnings should be greater than either Brent's or Julia's individual earnings, which is indeed the case. By carefully performing this addition and understanding its underlying principles, we have successfully solved the problem and gained a deeper understanding of the mathematical concepts involved.

Conclusion

In conclusion, Brent and Julia earned a total of $1320.00 from the sale of raffle tickets. This problem has provided a valuable exercise in applying basic arithmetic operations such as multiplication, division (in the context of fractions), and addition to solve a real-world scenario. By breaking down the problem into smaller, manageable steps, we were able to systematically calculate the earnings of each individual and then combine them to find the total. This step-by-step approach not only helps in arriving at the correct answer but also enhances problem-solving skills and the ability to think logically and methodically. Furthermore, this problem has reinforced the importance of understanding key mathematical concepts such as fractions and proportionality. Understanding these concepts is crucial for tackling more complex mathematical challenges in the future. The problem also highlights the practical applications of mathematics in everyday life, demonstrating how mathematical skills can be used to solve real-world problems involving money and finances. By mastering these fundamental mathematical skills, individuals can gain confidence in their abilities and apply them effectively in various situations, both academic and practical. In essence, this problem serves as a reminder that mathematics is not just an abstract subject but a powerful tool for understanding and navigating the world around us.