Calculating Instant Noodle Cartons A Mathematical Problem Solving Guide

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Introduction

In this article, we will delve into a mathematical problem involving Mr. Johnson, who imported cartons of instant noodles. Our goal is to determine the number of cartons he imported, given the number of packs per carton, the selling price of packs, and the total revenue received. This problem requires careful consideration of the relationships between quantities and prices, and we will break it down step by step to arrive at the solution. Understanding such mathematical problems not only enhances our problem-solving skills but also provides practical insights into real-world scenarios involving commerce and trade. We will explore the intricacies of this problem, ensuring that the solution is clear, concise, and easily understandable. This exploration is crucial for anyone looking to improve their quantitative reasoning and apply mathematical concepts in everyday situations. Let's embark on this mathematical journey to solve this intriguing problem and uncover the underlying principles that govern such calculations.

Problem Statement

Mr. Johnson imported a consignment of instant noodles. Each carton contained 28 packs of instant noodles. He sold 10 packs of instant noodles for five dollars. If he received a total of $280 from the sale of the instant noodles, the question we aim to answer is: how many cartons of instant noodles did Mr. Johnson import? This problem encapsulates basic principles of arithmetic, including multiplication and division, and requires a strategic approach to unravel the unknown. Understanding the problem statement is the first critical step towards finding a solution. We must identify the known quantities, such as the number of packs per carton, the selling price per pack, and the total revenue, and then use these to determine the unknown, which is the number of cartons. The problem's complexity lies in connecting these pieces of information logically. By carefully analyzing the given data, we can construct a mathematical framework to solve this real-world scenario. Let's proceed with the solution by first determining the total number of packs sold.

Step 1: Calculate the Total Number of Packs Sold

The first step in solving this problem is to determine the total number of packs of instant noodles that Mr. Johnson sold. We know that he received $280 from the sales, and he sold 10 packs for $5. To find the number of sets of 10 packs he sold, we can divide the total revenue by the price of 10 packs. This will give us the number of times he sold 10 packs. Mathematically, this can be represented as: Total Sets of 10 Packs Sold = Total Revenue / Price per 10 Packs. By substituting the given values, we get: Total Sets of 10 Packs Sold = $280 / $5 = 56 sets. Since each set contains 10 packs, we can now calculate the total number of packs sold by multiplying the number of sets by the number of packs in each set. Therefore, Total Packs Sold = 56 sets * 10 packs/set = 560 packs. This calculation is crucial as it bridges the gap between the total revenue and the number of individual packs sold. With this figure, we can proceed to determine the number of cartons required to hold these 560 packs, which is the ultimate goal of the problem. Understanding the relationship between revenue and units sold is a fundamental concept in commerce, and this step exemplifies its application in a practical scenario.

Step 2: Calculate the Number of Cartons

Now that we know Mr. Johnson sold a total of 560 packs of instant noodles, we can determine the number of cartons he imported. We are given that each carton contains 28 packs. To find the number of cartons, we need to divide the total number of packs sold by the number of packs per carton. This will give us the number of cartons required to hold all the packs. Mathematically, this can be represented as: Number of Cartons = Total Packs Sold / Packs per Carton. Substituting the values we have, we get: Number of Cartons = 560 packs / 28 packs/carton = 20 cartons. This calculation provides the final answer to our problem. Mr. Johnson imported 20 cartons of instant noodles. This step demonstrates the importance of understanding division as a tool for distributing a total quantity into equal groups. By dividing the total number of packs by the number of packs per carton, we have successfully determined the number of cartons. This final calculation is a testament to the logical sequence of steps we followed, starting from the total revenue and working our way back to the number of cartons. The entire process highlights the practical application of mathematical principles in solving real-world problems.

Conclusion

In conclusion, Mr. Johnson imported 20 cartons of instant noodles. We arrived at this solution by first calculating the total number of packs sold based on the revenue received and the selling price of 10 packs. We then divided the total number of packs sold by the number of packs per carton to find the number of cartons. This problem demonstrates the application of basic arithmetic principles in solving practical problems related to commerce and trade. The step-by-step approach we used is crucial for breaking down complex problems into manageable parts, making it easier to understand and solve. The ability to connect different pieces of information and use them strategically is a valuable skill in mathematics and beyond. By working through this problem, we have not only found the answer but also reinforced our understanding of how mathematical concepts can be applied in real-world scenarios. This exercise highlights the importance of quantitative reasoning and the ability to think critically when faced with numerical problems. We hope this detailed explanation has provided a clear understanding of the solution and the underlying mathematical principles involved. Understanding these types of problems not only enhances mathematical proficiency but also sharpens critical thinking and problem-solving skills that are applicable in various facets of life.

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