Question

Задача 10. Пиратская добыча Два пирата играли на золотые монеты. Игра состояла из трех партий: второй проиграл половину монет, имевшихся у него в начале игрыпервый проиграл половину от количества монет, образовавшегося у него после первой партиивторой проиграл половину от количества монет, образовавшегося у него после второй партии В результате у первого оказалось 24 монет, а у второго – 14. Сколько монет было у первого пирата до начала игры?

Answer 1

Начало: 1-й - x монет, 2-й - y монет
после 1 партии: 1-й - (x+y/2), 2-й - y/2
после 2 партии: 1-й - (x+y/2)/2, 2-й - y/2+(x+y/2)/2
после 3 партии:
1-й - (x+y/2)/2+(y/2+(x+y/2)/2)/2, 2-й - (y/2+(x+y/2)/2)/2
(x+y/2)/2+(y/2+(x+y/2)/2)/2 = 24,   (y/2+(x+y/2)/2)/2 = 14
(x+y/2)/2 = 10, (y/2+(x+y/2)/2)/2 = 14
x+y/2 = 20,  y/2+(x+y/2)/2 = 28
x+y/2 = 20,  y+(x+y/2) = 56
x+y/2 = 20,  y = 36
x = 2
Ответ: у первого пирата до начала игры было 2 монеты.

Answer 2

To solve this problem, let's break it down step by step.

Step 1: Define the variables

Let's assume that the number of coins the first pirate had at the beginning of the game is represented by x.

Step 2: Calculate the number of coins after each round

According to the problem, the second pirate lost half of the coins he had at the beginning of the game, and then the first pirate lost half of the coins he had after the first round. Finally, the second pirate lost half of the coins he had after the second round.

After the first round, the second pirate had x/2 coins left. After the second round, the first pirate had (x - (x/2))/2 coins left. After the third round, the second pirate had ((x - (x/2))/2)/2 coins left.

Step 3: Calculate the final number of coins

According to the problem, the first pirate had 24 coins left and the second pirate had 14 coins left after the three rounds.

Setting up the equations: - (x - (x/2))/2 = 24 - ((x - (x/2))/2)/2 = 14

Step 4: Solve the equations

Let's solve the equations to find the value of x.

Simplifying the first equation: - (x - (x/2))/2 = 24 - (2x - x)/2 = 24 - x/2 = 24 - x = 48

So, the first pirate had 48 coins at the beginning of the game.

I hope this helps! Let me know if you have any further questions.