Question

In the second week of the sale, the prices are reduced by 20% of the previous week's price. In the third week of the sale, the prices are again reduced by 20% of the previous week's price. This continues for 5 weeks. 5.6

2. Yaseen thinks this will mean that the prices will be reduced to $0 after the five reductions,

because 20% x 5 = 100%.

Please explain why Donkey is wrong.

Answer 1

Yaseen's calculation that 20% x 5 = 100% is correct, but the conclusion that the prices will be reduced to $0 after the five reductions is incorrect.

The reason for this is that each week, the price is reduced by 20% of the previous week's price, not the original price. So, after the first week, the price will be 80% of the original price, and after the second week, the price will be 80% of the price from the first week, which is 64% of the original price.

This means that the price after each week's sale is:

Week 1: 80% of the original price

Week 2: 64% of the original price

Week 3: 51.2% of the original price

Week 4: 40.96% of the original price

Week 5: 32.768% of the original price

As we can see, the prices will never be reduced to $0, but they will continue to decrease with each successive week of the sale.