Contextualization

Percentages are an essential part of our daily lives. Whether we are going to the market and see discounts, in the taxes we pay, or in the interest on debts and investments, we are always dealing with percentages. However, a concept that often causes confusion is that of successive percentages.

Theoretical introduction

In the world of percentages, 30% followed by another 30% does not always result in 60%. This is because percentages are always calculated based on the initial value. Therefore, if you discount 30% from a value and then discount another 30%, the second discount will be applied to the remaining value after the first discount, not to the total initial value. That's why it's important to understand successive percentages.

In successive percentages, each percentage is applied to the result of the previous calculation. It is important to remember that the order in which these percentages are applied can change the final result. For example, a 50% increase followed by a 50% decrease will not return to the initial value. This is because the second percentage is applied to the new value, after the first percentage has been applied.

Contextualization

In a practical situation, think of a store that is liquidating its clothing stock. After a first 20% discount, they decide to apply a second 10% discount on all items. This second discount is not applied to the original price of the item, but to the value with the first discount already applied. Therefore, if a pair of pants cost $100, after the first discount they will cost $80. The second 10% discount will then be $8, not $10 as it would be if applied to the original value.

This is a very relevant concept in real life and very useful for making financial decisions. Having the knowledge of how to calculate and understand successive percentages can help us make better choices when shopping, investing our money, or even when evaluating job offers.

Practical Activity - "Successive Discount Operation"

Project objective

In this project, students will create and manage an "online store" with a catalog of fictitious products, in which they will apply successive discounts to understand the real impact of successive percentages. In addition, they will explore and analyze marketing and economics strategies associated with the use of discounts and promotions.

Detailed project description

Teams (3 to 5 students) will begin by creating a list of products for the online store, each with its original price. Then, they will define a discount strategy for the store, including at least two successive discounts on all items. Then, they will have to calculate the final price of each item after applying the discounts.

The team must submit a project report, which must include an economic analysis section, considering aspects such as the impact of successive percentages on profits and sales, the possible reactions of customers to different discount strategies, and the implications for long-term business planning.

The team should also include a mathematical analysis section, detailing how the discounts were calculated, explaining the concept of successive percentages, and demonstrating how this concept was applied in their project.

Materials needed

• Computer with internet access
• Spreadsheet software (such as Excel)
• Notebook and pen for drafting

Detailed step-by-step

1. Meet with your team and create a catalog of products for the online store. Include at least 10 items, each with its original price.

2. Define a discount strategy for the store. This should include at least two successive discounts applied to all items.

3. Use a spreadsheet to calculate the final price of each item after applying the discounts. Your calculations should clearly demonstrate the concept of successive percentages.

4. Write an economic analysis section in your report. This section should consider how the discount strategy can affect the store's profit and sales, how customers might react to different discount strategies, and what the implications for long-term business planning are.

5. Write a mathematical analysis section in your report. This section should explain how the discounts were calculated, explain the concept of successive percentages, and demonstrate how this concept was applied in your project.

Project deliverables

• List of products with original and final prices after discounts
• Detailed discount strategy
• Spreadsheet with discount calculations
• Project report, including:
  • Introduction: Contextualization of the problem, project objectives and its relevance.
  • Development: Details of the project execution, calculations performed and discount strategy.
  • Conclusions: Reflections on the execution of the project, analysis of the results and lessons learned.
  • Bibliography: References used to prepare the project.

Remember that the writing of the report must be done in collaboration with all members of the group, each contributing to different sections. The writing of the report is a fundamental part of the project, as it is the opportunity to share your learnings and discoveries.