Question

Отец велел сыновьям собрать чайный лист с плантации, состоящей из 17 рядов. Старший сын должен обработать половину, средний-треть, а младший-девятую часть всех рядов. Братья не смогли разделить 17 рядов, как просил отец. На помощь пришел сосед. Он предложил им собрать чай еще с одного ряда на его плантации. Сколько рядов досталось каждому брату? Пришлось ли кому-либо из братьев собирать чай с плантации соседа?

Answer 1

9 6 2 не пришлосьсобирать

Answer 2

Problem Analysis

The problem states that there are 17 rows of tea leaves on a plantation, and the father instructed his three sons to divide the work among themselves. The eldest son should process half of the rows, the middle son should process one-third of the rows, and the youngest son should process one-ninth of the rows. However, the sons were unable to divide the 17 rows as instructed. A neighbor offered to help by allowing them to gather tea from an additional row on his plantation. The question is how many rows each brother received and whether any of them had to gather tea from the neighbor's plantation.

Solution

To solve this problem, we need to determine how many rows each brother received and whether any of them had to gather tea from the neighbor's plantation.

Let's calculate the number of rows each brother received:

- The eldest son should process half of the rows: 17 / 2 = 8.5 rows. - The middle son should process one-third of the rows: 17 / 3 = 5.67 rows. - The youngest son should process one-ninth of the rows: 17 / 9 = 1.89 rows.

Since we cannot have a fraction of a row, we need to round the numbers to the nearest whole number:

- The eldest son received 8 rows. - The middle son received 6 rows. - The youngest son received 2 rows.

Now, let's determine if any of the brothers had to gather tea from the neighbor's plantation. Since the total number of rows is 17 and the brothers received a total of 8 + 6 + 2 = 16 rows, there is one row left. Therefore, one of the brothers had to gather tea from the neighbor's plantation.

To determine which brother had to gather tea from the neighbor's plantation, we need to find out if 17 is divisible by 3, 9, or both. If it is divisible by 3, the middle son had to gather tea from the neighbor's plantation. If it is divisible by 9, the youngest son had to gather tea from the neighbor's plantation. If it is divisible by both 3 and 9, any of the two brothers could have gathered tea from the neighbor's plantation.

Let's check if 17 is divisible by 3 and 9:

- 17 % 3 = 2 (remainder) - 17 % 9 = 8 (remainder)

Since 17 is not divisible by either 3 or 9, we can conclude that one of the brothers had to gather tea from the neighbor's plantation, but it is not specified which brother.

Answer

Based on the calculations, each brother received the following number of rows:

- The eldest son received 8 rows. - The middle son received 6 rows. - The youngest son received 2 rows.

Additionally, one of the brothers had to gather tea from the neighbor's plantation, but it is not specified which brother.

Please let me know if there is anything else I can help you with!