Optimizing 100 Items for 100 Rupees: A Mathematical Approach

Imagine you have a budget of 100 rupees and you want to purchase a total of 100 items. The challenge is that each batch of 20 chocolates costs 1 rupee, and each wrapper costs another 5 rupees. How can you maximize the number of items you can buy with your budget? This intriguing problem has a fascinating solution that involves mathematical optimization.

Understanding the Problem

The problem can be expressed mathematically as follows:

Let C represent the number of chocolates. Let W represent the number of wrappers. Each 20 chocolates cost 1 rupee. Each wrapper costs 5 rupees. Our total budget is 100 rupees. Total items to be purchased is 100.

From the above conditions, we can establish the following two equations:

C W 100 (1)

C/20 5W 100 (2)

Solving the Problem Using Algebraic Methods

To solve these equations, we can use a step-by-step algebraic approach:

Multiply the first equation by 5 to align the terms for subtraction: 5(C W) 5(100) 5C 5W 500 (3) Subtract equation (3) from equation (2): (C/20 5W) - (5C 5W) 100 - 500 C/20 - 5C -400 (C - 100C) / 20 -400 -99C / 20 -400 -99C -8000 C 8000 / 99 C 80.81 ≈ 81 Substitute C back into equation (1) to find W: 81 W 100 W 19

Conclusion: Maximizing Your Budget

Using the above calculations, we can estimate that with a budget of 100 rupees, you can buy approximately 81 chocolates and 19 wrappers. However, in real scenarios, you need to round the values to the nearest whole numbers. Therefore, it is recommended to buy 81 chocolates and 19 wrappers to stay within the budget.

Note: The exact number might vary slightly based on rounding, but this approach ensures you get as close to 100 items as possible for 100 rupees.

Keyword Optimization

This article focuses on the keyword phrase mathematical optimization and related concepts such as budget allocation and cost minimization, which are key elements in solving such real-life problems. The problem of the chocolate wrapper also adds a unique twist, making it an interesting topic for SEO purposes.

Conclusion

By understanding the mathematical principles behind such problems, you can make better financial decisions and optimize your budget effectively. The chocolate wrapper problem is a practical example of applying algebraic methods to budget planning and cost management. Whether you're a student, a business owner, or just someone looking to manage your finances wisely, mastering this type of optimization can be incredibly valuable.