Understanding the Discount in a 'Buy 5 Get 2 Free' Offer

In today's competitive retail environment, many businesses offer promotional deals to incentivize customer purchases. One popular type of promotion is the 'buy 5 get 2 free' offer. This article delves into the detailed mechanics of this offer to help you understand the real discount percentage you are receiving. We'll walk through the mathematics behind it and provide a clear, step-by-step explanation of how to calculate the actual discount.

Breaking Down the 'Buy 5 Get 2 Free' Offer

The 'buy 5 get 2 free' offer means a customer purchases a total of 5 items (the paid items) and receives an additional 2 items for free (the free items). The total items received in this offer is 7. This can be visualized as follows:

Total items received: 7 5 bought 2 free

Calculating the Total Cost

Let's assume the price per item is P. Therefore, the total cost for the 5 items that you purchase is:

[ text{Total cost} 5P ] This total cost covers the price of 5 items, while the other 2 items are free.

Calculating the Cost Per Item in This Offer

To find the effective cost per item in this promotion, we need to divide the total cost by the total number of items received:

[ frac{5P}{7} text{ per item} ] This is the average cost per item when you consider that 2 items are free.

Determining the Discount Amount

The original price per item is P. Since you receive 2 free items, the discounted price per item (including the free items) is:

[ P - frac{5P}{7} frac{2P}{7} ] The discount amount per item is thus:

[ frac{2P}{7} ]

Calculating the Discount Percentage

To find the discount percentage, we use the formula:

[ text{Discount Percentage} frac{text{Discount Amount}}{text{Original Price}} times 100 ] Substituting the values we have: [ text{Discount Percentage} frac{frac{2P}{7}}{P} times 100 frac{2}{7} times 100 approx 28.57% ] So the effective discount offered in the 'buy 5 get 2 free' promotion is approximately 28.57%. This means that for every 7 items received, you are paying for 5 and getting the other 2 for free, resulting in a savings of 28.57% on the total value of the items purchased.

A Simplified Example

To illustrate this concept more clearly, let's use a simplified example. Assume the marked price (M.P.) of one item is 100. When you buy 5 items at 100 each, the total marked price is:

[ text{M.P. of 5 items} 5 times 100 500 ] However, under the 'buy 5 get 2 free' offer, you receive 2 additional items for free, making the total items received 7. If the price per item is still 100, the actual amount paid is:

[ text{Actually paid amount} 5 times 100 500 ] Even though you receive 7 items, you only pay for 5, so the discount is:

[ text{Discount} 500 - 400 200 ] The discount percentage is then calculated as:

[ frac{200}{700} times 100 28.57% ] Thus, you are getting a 28.57% effective discount on the total value of the items.

Conclusion

Understanding the true discount percentage in promotional offers like the 'buy 5 get 2 free' can help you make more informed purchasing decisions. Whether you are a consumer or a marketer, knowing the exact discount can help you maximize savings or calculate the desired promotional value.