Question

В ящике лежат арбузы. Сначала из него взяли половину всех арбузов и половину арбуза, затем половину остатка и ещё половину арбуза. Наконец, ещё достали половину нового остатка и половину арбуза. После этого в ящике остался 31 арбуз. Сколько арбузов было в ящике вначале?

Answer 1

                           Взяли                                                  осталось
 1.             x/2 +1/2 = (x+1)/2                                x - (x+1)/2 = (x-1)/2
 2.     (x - 1)/4 +1/2 = (x+1)/4                        (x-1)2 - (x+1)/4 = (x-3)/4
 3.     (x - 3)/8 +1/2 = (x+1)/8                       (x-3)/4 - (x+1)/8 = (x - 7)/8 
                                                  (x - 7)8 = 31
                                                     x = 255

Answer 2

(((31+0.5)*2+0.5)*2+0.5)*2=255

Answer 3

Problem Analysis

We are given the following information: - There are some watermelons in a box. - First, half of all the watermelons and half of a watermelon were taken out. - Then, half of the remaining watermelons and half of a watermelon were taken out. - Finally, half of the new remaining watermelons and half of a watermelon were taken out. - After all these operations, there were 31 watermelons left in the box.

We need to determine the initial number of watermelons in the box.

Solution

Let's work through the problem step by step:

1. Initially, let's assume there were x watermelons in the box. 2. After taking out half of all the watermelons and half of a watermelon, we are left with x/2 - 0.5 watermelons. 3. After taking out half of the remaining watermelons and half of a watermelon, we are left with (x/2 - 0.5)/2 - 0.5 watermelons. 4. After taking out half of the new remaining watermelons and half of a watermelon, we are left with ((x/2 - 0.5)/2 - 0.5)/2 - 0.5 watermelons. 5. According to the problem, the final number of watermelons left in the box is 31.

Now, we can set up an equation to solve for x:

((x/2 - 0.5)/2 - 0.5)/2 - 0.5 = 31

Let's solve this equation to find the initial number of watermelons in the box.

Calculation

((x/2 - 0.5)/2 - 0.5)/2 - 0.5 = 31

Simplifying the equation:

(x/2 - 0.5)/2 - 0.5 = 31 * 2

(x/2 - 0.5)/2 - 0.5 = 62

(x/2 - 0.5)/2 = 62 + 0.5

(x/2 - 0.5)/2 = 62.5

(x/2 - 0.5) = 62.5 * 2

(x/2 - 0.5) = 125

x/2 = 125 + 0.5

x/2 = 125.5

x = 125.5 * 2

x = 251

Answer

The initial number of watermelons in the box was 251.