Question

Ваня во столько раз старше своей сестры Ани, во сколько раз он моложе бабушки. Сколько лет Ване, если Ане нет ещё и 6 лет, а Ване вместе с бабушкой 112 лет? Возраст каждого - целое число лет. ДАЮ 28 БАЛЛОВ ПОМОГИТЕ СРОЧНО ПОЖАЛУЙСТА

Answer 1

6/Задание № 5:

Ваня во столько раз старше своей сестры Ани, во сколько раз он моложе бабушки. Сколько лет Ване, если Ане нет ещё и 6 лет, а Ване вместе с бабушкой 112 лет? Возраст каждого - целое число лет.

РЕШЕНИЕ: Пусть Ане x<6 лет. Тогда Ване kх лет, а бабушке - k^2x лет.

По условию Ване вместе с бабушкой 112 лет:

kx+k^2x=112

k(1+k)x=112

Если k=1, то k(1+k)=112, однако последовательных целых чисел, дающих в произведении 112 нет.

Если k=2, то k(1+k)=56, тогда k=7, kx=7*2=14 лет Ване

Если k=3, то k(1+k)=112/3 - не целое число

Если k=4, то k(1+k)=28, однако последовательных целых чисел, дающих в произведении 28 нет.

Если k=5, то k(1+k)=112/5 - не целое число

Единственный вариант, когда Ане 2 года и Ване 14 лет.

ОТВЕТ: 14 лет

Answer 2

Problem Analysis

We are given the following information: - Vanya is x times older than his sister Anya. - Vanya is y times younger than his grandmother. - Anya is 6 years old. - The combined age of Vanya and his grandmother is 112 years.

We need to find the age of Vanya.

Solution

Let's solve the problem step by step:

1. Let's assume that Vanya is x times older than Anya. Therefore, Vanya's age can be represented as x * Anya's age.

2. Similarly, let's assume that Vanya is y times younger than his grandmother. Therefore, Vanya's age can be represented as Grandmother's age / y.

3. We are given that Anya is 6 years old. So, Anya's age is 6.

4. We are also given that the combined age of Vanya and his grandmother is 112 years. Therefore, we can write the equation: Vanya's age + Grandmother's age = 112.

Now, let's substitute the values we have into the equation and solve for Vanya's age.

Calculation

Let's assume that Vanya is x times older than Anya and y times younger than his grandmother.

1. Vanya's age = x * Anya's age = x * 6.

2. Vanya's age = Grandmother's age / y.

3. Anya's age = 6.

4. Vanya's age + Grandmother's age = 112.

Substituting the values into the equation:

x * 6 + Grandmother's age / y = 112.

To solve this equation, we need to know the values of x and y.

Unfortunately, the given information does not provide the values of x and y. Therefore, we cannot determine the age of Vanya with the given information.

If you have any additional information or if there is anything else I can help you with, please let me know!