Question

Женя собрала в саду яблоки, чтобы выйти из сада ей пришлось пройти через 4 калитки, каждую из них охранял стражник, отбиравший половину яблок. Домой она принесла 10 яблок. Сколько яблок досталось каждому стражнику? Сколько яблок собрала в саду Женя?

Answer 1

Женя собрала 160 яблок: 
10*2=20
20*2=40
40*2=80
80*2=160

Answer 2

Problem Analysis

In this problem, we are given that Zhena collected apples in the garden and had to pass through four gates, each guarded by a guard who took half of her apples. We are also given that she brought 10 apples home. We need to determine how many apples each guard received and how many apples Zhena collected in the garden.

Solution

Let's assume that Zhena collected X apples in the garden.

When Zhena passed through the first gate, the guard took half of her apples, leaving her with X/2 apples. When Zhena passed through the second gate, the guard took half of her remaining apples, leaving her with (X/2)/2 = X/4 apples. When Zhena passed through the third gate, the guard took half of her remaining apples, leaving her with (X/4)/2 = X/8 apples. When Zhena passed through the fourth gate, the guard took half of her remaining apples, leaving her with (X/8)/2 = X/16 apples.

Finally, Zhena brought 10 apples home, so we have the equation:

X/16 = 10

To find the value of X, we can multiply both sides of the equation by 16:

X = 10 * 16 = 160

Therefore, Zhena collected 160 apples in the garden.

Now, let's calculate how many apples each guard received:

- The first guard received X/2 = 160/2 = 80 apples. - The second guard received (X/2)/2 = (160/2)/2 = 40 apples. - The third guard received ((X/2)/2)/2 = ((160/2)/2)/2 = 20 apples. - The fourth guard received (((X/2)/2)/2)/2 = (((160/2)/2)/2)/2 = 10 apples.

Therefore, each guard received 80, 40, 20, and 10 apples respectively.

Answer

Zhena collected 160 apples in the garden, and each guard received 80, 40, 20, and 10 apples respectively.