The beardless sly man Aldar-Kose lived in one aul. His eyes were sharp, his legs were quick, his hands were agile, and his mind was even more agile. Aldar-Kose loved to joke and laugh, especially at fools and misers. He had no wealth, but by cunning he did not get himself a meal of fat ram.
Zhatyr-bai was a greedy and stupid person. His flocks were large: he would start counting at dawn, and finish at dusk. Once Aldar-Kose came to him and said:
- Honorable buy, I have two rubles, but no wallet. I walk, hold the money in my hand - my hand is tired. I want to get rid of this money. Will you help me?
- Come on, come on, I will help! - buy was delighted. - Just tell me how?
“Sell me some poor little goat for two rubles,” says Aldar-Kose.
Thought, thought buy: "Well, you can sell." He caught a lame goat in the herd, skinny, barely alive, which had only two days left to die, and gave to Aldar-Kose:
- Here, take it, although it's a pity to give it away cheaply. Good kid. Give me two rubles!
Aldar-Kose took a goat, and keeps money in his fist:
- You know what, honorable buy. I changed my mind. Take two rubles and a kid to boot, and give me a lamb.
“Well, not a bad exchange,” thought Bay, “two rubles and even a kid to boot!” - and went to catch the lamb. Caught the smallest and serves Aldar-Kose:
- Here, take it. Nice lamb. Give me two rubles and a kid.
Aldar-Kose took the lamb, but he holds the money in his fist and does not let go of the goat:
- You know what, honorable buy. I changed my mind. Take two rubles, a kid and a lamb to boot, and give me a goat.
"Not a bad exchange," thought Bay, "two rubles and a goat, and even a lamb to boot." And he went to catch a goat. He caught the thinnest one and serves to Aldar-Kose:
- Here, take it, good goat. Give me two rubles, a kid and a lamb.
- Wait, wait, respectable bay! - says Aldar-Kose. - I changed my mind. Take two rubles, a kid, a lamb and a goat in addition, and give me only one ram, but let me choose it myself.
“This exchange is more profitable than all the others! - thought the delighted buy. - Two rubles, a kid, a lamb and even a goat to boot - and all this for one ram! And he says to Aldar-Kose:
- Well, choose!
He chose Aldar-Kose for himself the biggest, fatty ram, gave the bai two rubles, a kid, a lamb and a goat in addition, put the ram on his shoulders and went, and bai Zhatyr-bai laughed, rubbing his hands:
- What a fool Aldar-Kose! He gave so much good for just one ram!
Bay did not understand which of them was the fool.
Пусть Ф - сумма монет у Фомы.
Е - сумма монет у Ерёмы;
Ю - сумма монет у Юлия.
х - сумма монет Фома должен отдать Ерёме, чтобы у них было поровну.
Ф - х = Е + х
Если Фома отдаст Ерёме 70 монет, то у Ерёмы и Юлия будет поровну:
70 + Е = Ю
Если Фома отдаст Ерёме 40 монет, то у Фомы и Юлия будет поровну:
Ф - 40 = Ю
{ Ф - х = Е + х
{ 70 + Е = Ю
{ Ф - 40 = Ю
Получили систему из трех уравнений с 4-мя неизвестными:
{ Ф - 2х = Е (1)
{ 70 + Е = Ю (2)
{ Ф - 40 = Ю (3)
Сложим первые два уравнения:
Ф - 2х + 70 + Е = Е + Ю
Ф - 2х + 70 = Ю
Вычтем проученное уравнение из 3-го уравнение с третьим :
Ф - 40 - (Ф - 2х + 70) = Ю - Ю
Ф - 40 - Ф + 2х - 70 = 0
2х - 110 = 0
2х = 110
х = 110 : 2
х = 55 монет Фома должен отдать Ерёме, чтобы у них было поровну.
ответ: 55 монет.
Проверка:
{ Ф - 55 = Е + 55
{ 70 + Е = Ю
{ Ф - 40 = Ю
{ Ф = Е + 110
{ Е = Ю - 70 подставим в первое уравнение.
{ Ф = Ю + 40 подставим в первое уравнение.
Ю + 40 = Ю - 70 + 110
40 + 70 = 110
110 = 110
Пошаговое объяснение:
The beardless sly man Aldar-Kose lived in one aul. His eyes were sharp, his legs were quick, his hands were agile, and his mind was even more agile. Aldar-Kose loved to joke and laugh, especially at fools and misers. He had no wealth, but by cunning he did not get himself a meal of fat ram.
Zhatyr-bai was a greedy and stupid person. His flocks were large: he would start counting at dawn, and finish at dusk. Once Aldar-Kose came to him and said:
- Honorable buy, I have two rubles, but no wallet. I walk, hold the money in my hand - my hand is tired. I want to get rid of this money. Will you help me?
- Come on, come on, I will help! - buy was delighted. - Just tell me how?
“Sell me some poor little goat for two rubles,” says Aldar-Kose.
Thought, thought buy: "Well, you can sell." He caught a lame goat in the herd, skinny, barely alive, which had only two days left to die, and gave to Aldar-Kose:
- Here, take it, although it's a pity to give it away cheaply. Good kid. Give me two rubles!
Aldar-Kose took a goat, and keeps money in his fist:
- You know what, honorable buy. I changed my mind. Take two rubles and a kid to boot, and give me a lamb.
“Well, not a bad exchange,” thought Bay, “two rubles and even a kid to boot!” - and went to catch the lamb. Caught the smallest and serves Aldar-Kose:
- Here, take it. Nice lamb. Give me two rubles and a kid.
Aldar-Kose took the lamb, but he holds the money in his fist and does not let go of the goat:
- You know what, honorable buy. I changed my mind. Take two rubles, a kid and a lamb to boot, and give me a goat.
"Not a bad exchange," thought Bay, "two rubles and a goat, and even a lamb to boot." And he went to catch a goat. He caught the thinnest one and serves to Aldar-Kose:
- Here, take it, good goat. Give me two rubles, a kid and a lamb.
- Wait, wait, respectable bay! - says Aldar-Kose. - I changed my mind. Take two rubles, a kid, a lamb and a goat in addition, and give me only one ram, but let me choose it myself.
“This exchange is more profitable than all the others! - thought the delighted buy. - Two rubles, a kid, a lamb and even a goat to boot - and all this for one ram! And he says to Aldar-Kose:
- Well, choose!
He chose Aldar-Kose for himself the biggest, fatty ram, gave the bai two rubles, a kid, a lamb and a goat in addition, put the ram on his shoulders and went, and bai Zhatyr-bai laughed, rubbing his hands:
- What a fool Aldar-Kose! He gave so much good for just one ram!
Bay did not understand which of them was the fool.