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In a sale all the prices are reduced by 25%.Julie sees a jacket that costs $32 before the sale. How much does it cost in the sale? Show your calculations. In the second week of the sale, the prices are reduced by 25% of the previous week’s price.In the third week of the sale, the prices are again reduced by 25% of the previous week’s price.In the fourth week of the sale, the prices are again reduced by 25% of the previous week’s price.Julie thinks this will mean that the prices will be reduced to $0 after the four reductions because4 x 25% = 100%Is Julie correct or wrong? Justify with correct explanationIf Julie is able to buy her jacket after the four reductions, how much will she have to pay? Show your calculations.

Question

In a sale all the prices are reduced by 25%.Julie sees a jacket that costs 32beforethesale.Howmuchdoesitcostinthesale?Showyourcalculations. Inthesecondweekofthesale,thepricesarereducedby2532 before the sale. How much does it cost in the sale? Show your calculations. In the second week of the sale, the prices are reduced by 25% of the previous week’s price.In the third week of the sale, the prices are again reduced by 25% of the previous week’s price.In the fourth week of the sale, the prices are again reduced by 25% of the previous week’s price.Julie thinks this will mean that the prices will be reduced to 0 after the four reductions because4 x 25% = 100%Is Julie correct or wrong? Justify with correct explanationIf Julie is able to buy her jacket after the four reductions, how much will she have to pay? Show your calculations.

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Solution

Julie is incorrect. The reason is that each 25% reduction is not from the original price, but from the remaining price after the previous reduction. Here's how it works:

  1. In the first week, the jacket is reduced by 25% from 32.So,thereductionis25/10032=32. So, the reduction is 25/100 * 32 = 8. Therefore, the price after the first reduction is 32 - 8 = $24.

  2. In the second week, the jacket is reduced by 25% from the new price of 24.So,thereductionis25/10024=24. So, the reduction is 25/100 * 24 = 6. Therefore, the price after the second reduction is 24 - 6 = $18.

  3. In the third week, the jacket is reduced by 25% from the new price of 18.So,thereductionis25/10018=18. So, the reduction is 25/100 * 18 = 4.5. Therefore, the price after the third reduction is 18 - 4.5 = $13.5.

  4. In the fourth week, the jacket is reduced by 25% from the new price of 13.5.So,thereductionis25/10013.5=13.5. So, the reduction is 25/100 * 13.5 = 3.375. Therefore, the price after the fourth reduction is 13.5 - 3.375 = $10.125.

So, if Julie buys the jacket after the four reductions, she will have to pay $10.125.

This problem has been solved

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