Question

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

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 younger than Vanya. - The sum of Vanya's age and his grandmother's age is 112 years.

We need to find Vanya's age.

Solution

Let's break down the problem step by step:

1. Let's assume that Anya's age is a years. 2. According to the given information, Vanya is x times older than Anya. So, Vanya's age is x * a years. 3. Vanya is also y times younger than his grandmother. So, his grandmother's age is y * (x * a) years. 4. Anya is 6 years younger than Vanya. So, Anya's age is (x * a) - 6 years. 5. The sum of Vanya's age and his grandmother's age is 112 years. So, we have the equation: (x * a) + (y * (x * a)) = 112.

Now, we can solve this equation to find the values of x, y, and a.

Let's proceed with the calculations.

Calculation

Given: - Anya's age: a - Vanya's age: x * a - Grandmother's age: y * (x * a) - Anya's age (in terms of Vanya's age): (x * a) - 6 - Sum of Vanya's age and grandmother's age: (x * a) + (y * (x * a)) = 112

Substituting the values in the equation: (x * a) + (y * (x * a)) = 112

Simplifying the equation: x * a + x * y * a = 112

Factoring out a: a * (x + x * y) = 112

Dividing both sides by (x + x * y): a = 112 / (x + x * y)

Now, we can substitute the value of a back into the equation for Anya's age to find Vanya's age.

Answer

To find Vanya's age, we need to substitute the value of a back into the equation for Anya's age: (x * a) - 6.

Let's calculate the value of a using the given information.

According to the given information, Anya is 6 years younger than Vanya, and the sum of Vanya's age and his grandmother's age is 112 years.