Potato Sales Calculation Determining Sold And Remaining Weight

In this mathematical problem, we're diving into a real-world scenario involving a merchant and his sack of potatoes. The goal is to determine the total weight of potatoes sold and the amount remaining in the sack after several transactions. This exercise combines basic arithmetic operations, fractions, and units of measurement, offering a practical application of mathematical concepts. Let's break down the problem step by step and arrive at the solution.

(i) How many kg did he sell?

To determine the total weight of potatoes sold, we must sum the weights of each portion sold by the merchant. These portions are given as 6 kg, 5 1/4 kg, 9 1/2 kg, and 9 3/4 kg. The calculation involves adding whole numbers and fractions, which requires converting mixed fractions to improper fractions or decimals for ease of computation.

First, let's convert the mixed fractions to decimals. We have 5 1/4 kg, which is 5 + 1/4 = 5 + 0.25 = 5.25 kg. Next, 9 1/2 kg converts to 9 + 1/2 = 9 + 0.5 = 9.5 kg. Lastly, 9 3/4 kg is 9 + 3/4 = 9 + 0.75 = 9.75 kg. Now, we can add these values along with the 6 kg portion: 6 kg + 5.25 kg + 9.5 kg + 9.75 kg. Adding these figures together, we get 6 + 5.25 = 11.25 kg, then 11.25 + 9.5 = 20.75 kg, and finally, 20.75 + 9.75 = 30.5 kg. Therefore, the merchant sold a total of 30.5 kg of potatoes. This calculation demonstrates the importance of understanding fractions and decimals in practical scenarios, particularly in business and trade where accurate measurements are crucial. It's a fundamental concept in mathematics that applies directly to everyday situations. The ability to quickly and accurately perform these calculations can help in inventory management, sales tracking, and ensuring fair transactions. Moreover, it highlights the relevance of mathematical skills in commerce and the importance of precision in measurements. The merchant's sales, in this instance, reflect a significant portion of his initial stock, and this kind of calculation is vital for managing resources effectively. Understanding these principles helps not just in academic pursuits but also in practical business management and financial planning. Therefore, the merchant's total sales of potatoes amount to 30.5 kg, showing how essential basic mathematical skills are for real-world applications.

(ii) How many kg are still left in the sack?

To find the remaining weight of potatoes in the sack, we subtract the total weight sold from the initial weight. The merchant started with a sack of potatoes weighing 120 kg, and we've calculated that he sold 30.5 kg. Therefore, we need to subtract 30.5 kg from 120 kg: 120 kg - 30.5 kg. This subtraction is a straightforward arithmetic operation, but it's crucial to ensure accuracy in the calculation to correctly determine the remaining stock.

Performing the subtraction, 120 - 30.5, we get 89.5 kg. This means that after selling portions totaling 30.5 kg, the merchant has 89.5 kg of potatoes left in the sack. This result is vital for inventory management, allowing the merchant to know exactly how much stock he has available for future sales. Effective stock management is essential in any business to avoid shortages or overstocking, both of which can lead to financial losses. Understanding the quantity of goods on hand helps in making informed decisions about purchasing, pricing, and marketing strategies. It's also crucial for planning and forecasting future sales, as the merchant can estimate how long the remaining stock will last based on his average sales rate. Furthermore, this calculation highlights the practical application of subtraction in real-world scenarios, demonstrating its importance in managing resources and tracking inventory. The remaining 89.5 kg represents a significant portion of the initial stock, indicating that the merchant still has a substantial quantity of potatoes to sell. This understanding is critical for operational planning and ensuring that customer demand can be met. The ability to accurately calculate remaining stock is a fundamental skill in retail and other businesses involving physical goods. This process not only ensures efficient business operations but also contributes to financial stability by optimizing resource use and minimizing potential losses. Therefore, the merchant has 89.5 kg of potatoes remaining in the sack, underscoring the importance of basic arithmetic in business and inventory management.

In summary, the merchant sold a total of 30.5 kg of potatoes, and he has 89.5 kg remaining in the sack. This problem illustrates how essential basic mathematical skills are in everyday scenarios, especially in business. Calculating sales and remaining stock is a fundamental aspect of inventory management and helps ensure efficient and profitable operations. The ability to work with fractions, decimals, and perform basic arithmetic operations is not just a classroom exercise but a practical necessity for anyone involved in commerce and trade. This exercise also reinforces the idea that mathematics is a tool that helps us make informed decisions and manage resources effectively in real-world situations.