Calculating the Number of Sports Jerseys Purchased with a Discount

Introduction

If you're a shopkeeper selling sports jerseys, applying discounts can be a great way to boost sales and customer satisfaction. For instance, a shopkeeper sells sports jerseys at 10 EUR each, but applies a 10% discount starting from the tenth jersey. This scenario leads to various discount tiers, making the total cost per jersey variable. In this article, we will solve a practical problem involving this scenario to better understand the calculations involved.

Problem Statement

A team paid 153 EUR for a certain number of sports jerseys, taking advantage of the 10% discount on each jersey starting from the tenth one.

Solution Approach

To find out how many jerseys the team bought, let's use algebraic and logical steps to solve the problem. We will break down the calculation into several parts and ensure step-by-step clarity.

Step-by-Step Calculation

Let's denote:

D as the discount, which is 10% (0.10). S.p as the sale price, which is 10 EUR - (10 * 0.10) 9 EUR for each jersey starting from the tenth one.

Let the number of jerseys bought be y. The first 9 jerseys are sold at 10 EUR each, and any remaining jerseys (starting from the tenth one) are sold at 9 EUR each.

Calculate the cost for the first 9 jerseys:

9 jerseys × 10 EUR per jersey 90 EUR

Let x be the number of jerseys bought with the discount, which is 9 - 10 7 jerseys.

Calculate the cost for the discounted jerseys starting from the tenth one:

7 jerseys × 9 EUR per jersey 63 EUR

The total cost for the jerseys is:

90 EUR 63 EUR 153 EUR

In total, the team bought 9 7 16 jerseys.

Explanation and Conclusion

By breaking down the problem, we can see that the team bought a total of 16 jerseys. The first 9 jerseys were sold at the full price, and the subsequent 7 jerseys were sold with a 10% discount. This approach works for any such scenario where discounts are applied after a certain threshold.

Additional Insights

The problem-solving method discussed here can be applied to other similar scenarios involving tiered pricing or discounts. By understanding how to handle discounts on different tiers, it is easier to calculate total costs and make informed business decisions.

Conclusion

Understanding how to calculate the total cost of goods sold with tiered pricing is crucial for retail and e-commerce businesses. If you are a shopkeeper or a buyer, knowing how to apply discounts and calculate the total cost can significantly improve your business operations and customer satisfaction.