Question

Предложил чёрт лодырю:"Всякий раз,как перейдёшь этот волшебный мост,твои деньги удвоятся.За это ты перейдя мост,должен будешь отдать мне 24 копейки."Трижды перешёл лодырь мост-и остался совсем без денег ( то есть в третий раз отдал чёрту точно не те 24 копейки, что остались у него к этому моменту).Сколько денег было у лодыря перевоначально?

Answer 1

Пусть х копеек было денег
тогда
1- проход через мост:

$2x-24$

2-проход через мост

$2(2x-24)-24=4x-48-24=4x-72$

3-проход через мост

$2(4x-72)-24=8x-144-24=8x-168$

и денег не осталось

$8x-168=0 8x= 168 x= 168:8 x=21$

Значит денег было 21 копейка

Проверим: 

$21*2-24 = 42-24=18 18*2-24= 12 12*2-24=0$

Ответ: 21 копейка

Answer 2

Problem Analysis

The problem states that a devil offered a beggar a deal: every time the beggar crosses a magical bridge, his money will double. However, each time he crosses the bridge, he must give the devil 24 kopecks. The beggar crossed the bridge three times and ended up with no money. We need to determine how much money the beggar initially had.

Solution

Let's analyze the situation step by step:

1. The beggar starts with some initial amount of money. 2. After crossing the bridge for the first time, his money doubles, but he gives 24 kopecks to the devil. 3. After crossing the bridge for the second time, his money doubles again, but he gives another 24 kopecks to the devil. 4. After crossing the bridge for the third time, his money doubles once more, but he gives the devil another 24 kopecks.

To find the initial amount of money the beggar had, we need to work backward from the final result of having no money.

Let's denote the initial amount of money as x.

After the first crossing, the beggar has 2x - 24 kopecks remaining. After the second crossing, he has 2(2x - 24) - 24 kopecks remaining. After the third crossing, he has 2(2(2x - 24) - 24) - 24 kopecks remaining.

According to the problem, the beggar ends up with no money after the third crossing. So we can set up the following equation:

2(2(2x - 24) - 24) - 24 = 0

Now, let's solve this equation to find the initial amount of money x.

Calculation

Simplifying the equation:

2(2(2x - 24) - 24) - 24 = 0

Expanding the brackets:

2(4x - 48 - 24) - 24 = 0

2(4x - 72) - 24 = 0

Distributing the 2:

8x - 144 - 24 = 0

8x - 168 = 0

Adding 168 to both sides:

8x = 168

Dividing both sides by 8:

x = 21

Answer

The initial amount of money the beggar had was 21 kopecks.