Question

Петя и Вася поочерёдно берут конфеты из одного пакета.Петя берёт 1 кофету ВАСЯ 4 и т.д. Когда количество оставшихся в пакете конфет станет меньше необходимого тот чья очередь берет оставшиеся конфеты . Сколько было конфет первоначально если у пети в итоге оказалось 101 конфета ?

Answer 1

(101-3)×4=392+3+101=496(к)

Answer 2

Problem Analysis

In this problem, Petya and Vasya take turns taking candies from a bag. Petya takes 1 candy, Vasya takes 4 candies, and so on. The game continues until the number of candies remaining in the bag is less than the required amount for the next turn. At that point, the person whose turn it is takes the remaining candies. We need to determine the initial number of candies in the bag if Petya ends up with 101 candies.

Solution

Let's work through the problem step by step.

1. Petya takes 1 candy, leaving the bag with `x - 1` candies. 2. Vasya takes 4 candies, leaving the bag with `(x - 1) - 4 = x - 5` candies. 3. Petya takes 9 candies, leaving the bag with `(x - 5) - 9 = x - 14` candies. 4. Vasya takes 16 candies, leaving the bag with `(x - 14) - 16 = x - 30` candies.

We can see that the number of candies remaining in the bag after each turn follows the pattern: `x - 1`, `x - 5`, `x - 14`, `x - 30`, and so on.

Let's continue this pattern until we reach a point where the number of candies remaining is less than the required amount for the next turn.

5. Petya takes 25 candies, leaving the bag with `(x - 30) - 25 = x - 55` candies. 6. Vasya takes 36 candies, leaving the bag with `(x - 55) - 36 = x - 91` candies. 7. Petya takes 49 candies, leaving the bag with `(x - 91) - 49 = x - 140` candies. 8. Vasya takes 64 candies, leaving the bag with `(x - 140) - 64 = x - 204` candies.

At this point, the number of candies remaining in the bag is less than the required amount for the next turn. So, it's Petya's turn to take the remaining candies.

9. Petya takes `(x - 204)` candies.

According to the problem statement, Petya ends up with 101 candies. Therefore, we can set up the following equation:

x - 204 = 101

Solving this equation will give us the initial number of candies, `x`.

Calculation

Let's solve the equation:

x - 204 = 101

Adding 204 to both sides:

x = 101 + 204
x = 305

Therefore, the initial number of candies in the bag was 305.

Answer

The initial number of candies in the bag was 305.