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 problem where there is 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.

Solution

Let's break down the problem 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. Let's find the prime numbers less than 50 and check if their digit sum is 11. - From source we can see that the prime numbers less than 50 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and 47. - Checking the digit sum of these numbers, we find that the only number with a digit sum of 11 is 29.

2. 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. Let's use algebra to represent these relationships. - 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. - The number of green balls is 13 less than the number of yellow balls, so it is y - 13.

3. We know that the total number of balls is 29. We can write an equation to represent this: - Total number of balls = Number of red balls + Number of yellow balls + Number of green balls - 29 = 2y + y + (y - 13) - Simplifying the equation, we get: - 29 = 4y - 13 - 42 = 4y - y = 10.5

4. Since the number of balls cannot be a decimal, we can conclude that there is no solution to this problem.

Conclusion

Based on the given information, there is no solution to the problem. The number of green balls cannot be determined.