Question

Папа купил на праздник своим детям коробку конфет. Федя взял половину конфет и половинку одной конфеты, Аня взяла половину остатка и ещё полконфеты. Коля взял половину нового остатка и ещё полконфеты. Маша взяла половину оставшихся конфет и ещё пол конфеты. После этого в коробке осталась одна конфета. Сколько конфет было в коробке?

Answer 1

Х-0,5х-0,25х-0,125х-0,0625х-2=1
х-2-0,9375х=1
0,0625х-2=1
0,0625х=3
х=3/0,0625=48
Відповідь: в коробці було 48 цукерок

Answer 2

Problem Analysis

In this problem, we are given a scenario where a father buys a box of candies for his children on a holiday. Each child takes a certain portion of the candies, and we need to determine the initial number of candies in the box.

Solution

Let's break down the information given in the problem step by step:

1. The father bought a box of candies for his children on a holiday. 2. Fyodor (Fедя) took half of the candies and half of one more candy. 3. Anya (Аня) took half of the remaining candies and half of one more candy. 4. Kolya (Коля) took half of the new remaining candies and half of one more candy. 5. Masha (Маша) took half of the remaining candies and half of one more candy. 6. After all the children took their share, there was one candy left in the box.

To find the initial number of candies in the box, we can work backward from the final step:

1. After Masha took her share, there was one candy left in the box. 2. Masha took half of the remaining candies and half of one more candy. - Let's assume the number of candies Masha took is represented by x. - So, Masha took (x/2) + 0.5 candies. - After Masha took her share, the remaining candies in the box would be (x/2) - 0.5. 3. Kolya took half of the new remaining candies and half of one more candy. - Kolya took ((x/2) - 0.5)/2 + 0.5 candies. - After Kolya took his share, the remaining candies in the box would be ((x/2) - 0.5)/2 - 0.5. 4. Anya took half of the remaining candies and half of one more candy. - Anya took (((x/2) - 0.5)/2 - 0.5)/2 + 0.5 candies. - After Anya took her share, the remaining candies in the box would be (((x/2) - 0.5)/2 - 0.5)/2 - 0.5. 5. Fyodor took half of the remaining candies and half of one more candy. - Fyodor took ((((x/2) - 0.5)/2 - 0.5)/2 - 0.5)/2 + 0.5 candies. - After Fyodor took his share, the remaining candies in the box would be ((((x/2) - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5.

Since we know that after all the children took their share, there was one candy left in the box, we can set up the following equation:

((((x/2) - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 = 1

Now, let's solve this equation to find the value of x and determine the initial number of candies in the box.

Calculation

Simplifying the equation:

((((x/2) - 0.5)/2 - 0.5)/2 - 0.5)/2 - 0.5 = 1

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

((x/2) - 0.5)/2 - 0.5 = 4

(x/2) - 0.5 = 8

x/2 = 8.5

x = 17

Therefore, the initial number of candies in the box was 17.

Answer

The initial number of candies in the box was 17.