Question

Два книжных магазина имеют в продаже одну и ту же книгу. Через неделю в первом магазине цены на эту книгу были снижены на 10 %, а еще через неделю – подняты на 20 %. Во втором магазине через две недели цены на книгу были увеличены на 10%. В каком из магазинов через две недели цены на книгу стали ниже?

Answer 1

Решение:
Обозначим первоначальную цену книги за (х) руб как в первом так и во втором магазине (так как судя по вопросу, цена на книгу в обоих магазинах была одинаковой),
тогда в первом магазине:
после снижения цены на 10%, цена книги стала равной:
х-10%*х:100%=х-0,1х=0,9х (руб)
после повышения цены на 20%,  цена книги стала составлять:
0,9х+20%*0,9х:100=0,9х+0,18х=1,08х

во втором магазине после повышения цены на 10%, цена книги стала равной:
х+10%*х:100%=х+0,1х=1,1х
Если сравнить цены книги в первом и во втором магазине, то мы увидим, что в первом магазине цена на книгу стала ниже чем во втором магазине:
1,08х<1,1x

Answer 2

Problem Analysis

We have two bookstores selling the same book. The first store reduces the price of the book by 10% after one week and then increases it by 20% after another week. The second store increases the price of the book by 10% after two weeks. We need to determine in which store the price of the book becomes lower after two weeks.

Solution

Let's assume the original price of the book is P.

In the first store: - After one week, the price of the book is reduced by 10%, which means the new price is 0.9P. - After another week, the price of the book is increased by 20%, which means the new price is 1.2(0.9P) = 1.08P.

In the second store: - After two weeks, the price of the book is increased by 10%, which means the new price is 1.1P.

To determine in which store the price of the book becomes lower after two weeks, we need to compare the prices in both stores.

If 1.08P < 1.1P, then the price in the first store is lower after two weeks. If 1.08P > 1.1P, then the price in the second store is lower after two weeks.

Let's calculate the result:

1.08P < 1.1P

Since P is positive, we can divide both sides of the inequality by P:

1.08 < 1.1

The inequality is true, which means the price in the first store is lower after two weeks.

Answer

After two weeks, the price of the book becomes lower in the first store.

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