Question

У Ани вдвое больше карандашей, чем у Кати, а у Саши на 13 карандашей меньше, чем у Кати. Если пересчитать все карандаши, то получится простое число, которое меньше 50, сумма цифр которого равна 11. Сколько карандашей у Кати

Answer 1

Ответ 15 карандашей у Кати

Answer 2

Ответ 47 так как 47 больше 50 и 4+7=11

Answer 3

У Ани вдвое больше карандашей, чем у Кати, а у Саши на 13 карандашей меньше, чем у Кати. Если пересчитать все карандаши, то получится простое число, которое меньше 50, сумма цифр которого равна 11. Нам нужно найти количество карандашей у Кати.

Step 1: Analyzing the information given

Let's break down the information given: - У Ани вдвое больше карандашей, чем у Кати (Anya has twice as many pencils as Katya). - У Саши на 13 карандашей меньше, чем у Кати (Sasha has 13 pencils fewer than Katya). - Если пересчитать все карандаши, то получится простое число, которое меньше 50, сумма цифр которого равна 11 (If we count all the pencils, we get a prime number less than 50, and the sum of its digits is 11).

Step 2: Solving the problem

To find the number of pencils Katya has, we can use a trial and error approach. We'll start with a number less than 50 and check if it meets the given conditions.

Let's assume Katya has 20 pencils. According to the given information: - Anya has twice as many pencils as Katya, so Anya has 40 pencils. - Sasha has 13 pencils fewer than Katya, so Sasha has 7 pencils.

Now, let's count all the pencils: 20 + 40 + 7 = 67. This is not a prime number, so our assumption is incorrect.

Let's try another number. Assuming Katya has 10 pencils: - Anya has twice as many pencils as Katya, so Anya has 20 pencils. - Sasha has 13 pencils fewer than Katya, so Sasha has -3 pencils. Since we can't have a negative number of pencils, this assumption is incorrect.

Let's try one more number. Assuming Katya has 30 pencils: - Anya has twice as many pencils as Katya, so Anya has 60 pencils. - Sasha has 13 pencils fewer than Katya, so Sasha has 17 pencils.

Now, let's count all the pencils: 30 + 60 + 17 = 107. This is a prime number, and the sum of its digits is 11.

Therefore, Katya has 30 pencils.

Conclusion

Based on the given information, Katya has 30 pencils.