Math CentralQuandaries & Queries


Question from Tiffany, a student:

Khairul wants to buy a sofa set. He is offered 3 successive discounts of 10%,20% and 25%, and he can arrange them in any order he wants. Which order will benefit him the most? Explain your answer.

Hi Tiffany,

Suppose the price of the sofa before any discounts is $\$p.$ I am going to apply the discounts in the order you have in your question.

The first discount is 10% so the price after the first discount is 90% of the original price, that is $0.90 \times \$p.$ The second discount is 20% of the first discounted price so the price after the second discount is 80% of the first discounted price, that is $0.80 \times 0.90 \times \$p.$ What is the price after the third discount of 25%?

There are 6 different orders to apply the discounts. Choose another and see the final price after the three discounts. How does it compare to the final price in the order I chose?


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