Question

В коробке лежат красные, жёлтые и зелёные шарики. Общее число шариков - простое число, которое меньше, чем 50, сумма цифр которого равна 11. Красных шариков вдвое больше, чем жёлтых, а зелёных на 13 меньше, чем жёлтых. Сколько зелёных шариков?

Answer 1

6/Задание № 4:

В коробке лежат красные, жёлтые и зелёные шарики. Общее число шариков - простое число, которое меньше, чем 50, сумма цифр которого равна 11. Красных шариков вдвое больше, чем жёлтых, а зелёных на 13 меньше, чем жёлтых. Сколько зелёных шариков?

РЕШЕНИЕ: Пусть зеленых шариков х. Тогда, желтых шариков (х+13) штук, а красных шариков 2(х+13).

Общее число шариков:

х+(х+13)+2(х+13)=х+х+13+2х+26=4х+39

Если х=1, то 4х+39=43 - не подходит под условие

Если х=2, то 4х+39=47 - подходит под условие: простое число с суммой цифр 11

Если х=3 и более, то 4х+39=51 и более - не подходит под условие

ОТВЕТ: 2

Answer 2

Problem Analysis

We are given a box containing red, yellow, and green balls. The total number of balls is a prime number less than 50, and the sum of its digits is 11. The number of red balls is twice the number of yellow balls, and the number of green balls is 13 less than the number of yellow balls. We need to determine the number of green balls in the box.

Solution

Let's analyze the given information step by step to find the solution.

1. The total number of balls is a prime number less than 50, and the sum of its digits is 11. - The sum of the digits of a number is 11, and the number is less than 50. - From the given information, we can conclude that the total number of balls is 29. 2. The number of red balls is twice the number of yellow balls. - Let's assume the number of yellow balls is y. - The number of red balls is twice the number of yellow balls, so it is 2y.

3. The number of green balls is 13 less than the number of yellow balls. - The number of green balls is y - 13.

4. We need to determine the number of green balls. - From the above information, we know that the number of green balls is y - 13.

To find the number of green balls, we need to find the value of y. Let's solve for y using the given information.

The total number of balls is 29, which is a prime number. The possible values for y can be 3, 5, 7, 11, 13, 17, 19, or 23. However, we need to find a value of y that satisfies the condition that the number of green balls is y - 13.

Let's check each possible value of y:

- If y = 3, then the number of green balls is 3 - 13 = -10, which is not possible. - If y = 5, then the number of green balls is 5 - 13 = -8, which is not possible. - If y = 7, then the number of green balls is 7 - 13 = -6, which is not possible. - If y = 11, then the number of green balls is 11 - 13 = -2, which is not possible. - If y = 13, then the number of green balls is 13 - 13 = 0, which is possible. - If y = 17, then the number of green balls is 17 - 13 = 4, which is possible. - If y = 19, then the number of green balls is 19 - 13 = 6, which is possible. - If y = 23, then the number of green balls is 23 - 13 = 10, which is possible.

From the above analysis, we can see that the possible values for the number of green balls are 0, 4, 6, and 10.

Therefore, there can be 0, 4, 6, or 10 green balls in the box.

Answer

The number of green balls in the box can be 0, 4, 6, or 10.