Question

Иванов, Петров ,Сидоров сыграли три партии, причем проигравший обязан был удваивать суммы принадлежащие остальным вначале партии. Проиграли последовательно Иванов, Петров и Сидоров и в результате у всех троих оказалось по 48 рублей. Сколько денег было у каждого из них перед игрой? ​

Answer 1

Пусть в некоторый момент у Иванова, Петрова и Сидорова по x, y, z рублей. Тогда предыдущая расстановка имела вид x/2, y/2, z+x/2+y/2. Зная это, решим задачу с конца: (48, 48, 48) ←(24, 24, 96)←(12, 84, 48)←(78, 42, 24).

Ответ: У Иванова было 78 рублей, у Петрова 42, у Сидорова 24

Answer 2

Ответ:

Иванов = 78 руб

Петров = 42 руб

Сидоров = 24 руб

Пошаговое объяснение:

Решение:

Рассмотрим ситуацию с конца:

После 3-ей партии:

Иванов = 48 руб

Петров = 48 руб

Сидоров = 48 руб

После 2-ой партии:

Иванов = 48 ÷ 2 = 24 руб

Петров = 48 ÷ 2 = 24 руб

Сидоров = 48 + 24 + 24 = 96 руб

После 1-ой партии:

Иванов = 24 ÷ 2 = 12 руб

Петров = 24 + 12 + 48 = 84 руб

Сидоров = 96 ÷ 2 = 48 руб

До начало игры:

Иванов = 12 + 42 + 24 = 78 руб

Петров = 84 ÷ 2 =42 руб

Сидоров = 48 ÷ 2 = 24 руб

Ответ:

Иванов = 78 руб

Петров = 42 руб

Сидоров = 24 руб

Answer 3

#### Problem Analysis Three players, Ivanov, Petrov, and Sidorov, played three games. The loser of each game had to double the amount of money owned by the other two players at the beginning of the game. In the end, all three players had a total of 48 rubles. We need to determine how much money each player had before the game. #### Solution Let's assume that Ivanov, Petrov, and Sidorov had x, y, and z rubles respectively before the game. According to the given conditions: - Ivanov lost the first game and doubled the amount of money owned by Petrov and Sidorov. Therefore, Ivanov had x - 2y - 2z rubles after the first game. - Petrov lost the second game and doubled the amount of money owned by Ivanov and Sidorov. Therefore, Petrov had y - 2(x - 2y - 2z) - 2z rubles after the second game. - Sidorov lost the third game and doubled the amount of money owned by Ivanov and Petrov. Therefore, Sidorov had z - 2(x - 2y - 2z) - 2(y - 2(x - 2y - 2z)) rubles after the third game. Given that the total amount of money owned by all three players after the games is 48 rubles, we can set up the following equation: (x - 2y - 2z) + (y - 2(x - 2y - 2z) - 2z) + (z - 2(x - 2y - 2z) - 2(y - 2(x - 2y - 2z))) = 48 Simplifying the equation will give us the values of x, y, and z. #### Calculation Let's solve the equation to find the values of x, y, and z. (x - 2y - 2z) + (y - 2(x - 2y - 2z) - 2z) + (z - 2(x - 2y - 2z) - 2(y - 2(x - 2y - 2z))) = 48 Simplifying the equation step by step: x - 2y - 2z + y - 2x + 4y + 4z + z - 2x + 4y + 4z - 4x + 8y + 8z = 48 -5x + 17y + 18z = 48 Now, we can solve this equation to find the values of x, y, and z. #### Solution Using the equation -5x + 17y + 18z = 48, we can find the values of x, y, and z. Let's solve the equation: -5x + 17y + 18z = 48 To find the values of x, y, and z, we need more information or additional equations. The given information is not sufficient to determine the exact values of x, y, and z. Therefore, without additional information, we cannot determine how much money each player had before the game. If you have any additional information or equations, please provide them, and I will be happy to help you further.