Decoding the Mystery of Mobile Phone Discounts: A Step-by-Step Analysis

Often, when you're shopping for a mobile phone, you encounter a range of discounts that can make the final price seem confusing. In this article, we'll unravel the mystery behind successive discounts by using a real-life example. We'll also provide step-by-step solutions to understand the original selling price of the mobile phone, applying mathematical concepts along the way.

Understanding Successive Discounts

The example provided involves a mobile phone that had three successive discounts of 25% each. The final price is given as $13.5 after these discounts. To tackle this problem, we'll use a combination of mathematical operations and practical retail knowledge.

Simplifying the Problem

Sometimes, a 25% discount is the same as multiplying the price by 75% (or 0.75). This conversion can simplify the calculation. Let's denote the original selling price of the mobile phone as OSP.

Step-by-Step Calculation

Step 1: Calculate the price after the first 25% discount. OSP - 25% of OSP 0.75 * OSP

Step 2: Calculate the price after the second 25% discount. 0.75 * OSP - 25% of 0.75 * OSP 0.75 * OSP - 0.1875 * OSP 0.5625 * OSP

Step 3: Calculate the price after the third 25% discount. 0.5625 * OSP - 25% of 0.5625 * OSP 0.5625 * OSP - 0.140625 * OSP 0.421875 * OSP

Now, this final price is equal to $13.5.

Mathematical Representation

Thus, we have the equation:

0.421875 * OSP 13.5

Solving for OSP:

OSP 13.5 / 0.421875

getResultBy: OSP 32

Step 4: Verify the result by performing the inverse calculation.

Let's perform the calculation to verify:

32 * 0.75 24

24 * 0.75 18

18 * 0.75 13.5

Alternative Approach

Another approach to understanding this problem is by using the concept of percentage increase. If a price is decreased by 25%, it is effectively reduced to 75% of its previous value. If you want to reverse the effect of a 25% discount, you must calculate the original price by increasing the final price by a certain factor.

Step 1: Start with the final price after three discounts of $13.5.

Step 2: Calculate the original price using:

Original Price Final Price / (0.75 * 0.75 * 0.75)

Original Price 13.5 / 0.421875

Calculating this, we get:

Original Price 32

Alternative Method Using Percentage Increase

Another method to understand the problem is through the concept of percentage. A discount of 25% can be represented as a 75% decrease. To find the original price, you can use the following steps:

Step 1: Start with the final price after three discounts, $13.5.

Step 2: Calculate the original price by dividing the final price by the cumulative discount factor:

OSP 13.5 / (0.75 * 0.75 * 0.75)

OS 13.5 / 0.421875

OS 32

Conclusion

Understanding successive discounts requires careful calculation and a clear understanding of percentage concepts. By following the steps outlined above, we can determine that the original selling price of the mobile phone was $32. This method can be applied to other scenarios where successive discounts are involved, making it a valuable tool for both consumers and retailers.

Frequently Asked Questions

Q: How can I apply these calculations to other products?

A: The same method can be applied to other products, whether you are dealing with mobile phones, electronics, or any other goods that offer successive discounts. Just replace the values with the actual prices and apply the same discount percentages.

Q: What if the discount percentages are different?

A: If the discount percentages are different, you can calculate the cumulative discount factor in a similar way. For example, if there are discounts of 20%, 30%, and 40%, the cumulative factor would be (1 - 0.20) * (1 - 0.30) * (1 - 0.40).

Additional Resources

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