Question

Известно что сумма возрастов маши и ее братьев равна 65 годам. Егор старше Маши на 7 лет и в 2 раза старше Антона. Определите возраст каждого.

Answer 1

Раскладываем на множители 1664:
2 2 2 2 2 2 2 13 (7 двоек и 13).
При 2ух братьях невозможно 13 (возраст отличается вдвое и 13 должно входить в оба возраста)
Поэтому возрастов три:
13 лет и оставшиеся 7 двоек разделяем - одному 4 двойки (произведение) , другому-3.
13 8 и 16 лет, произведение сходится! ТРИ брата!

Answer 2

Problem Analysis

We are given that the sum of the ages of Masha and her brothers is 65 years. We also know that Egor is 7 years older than Masha and twice as old as Anton. We need to determine the age of each person.

Solution

Let's assign variables to the ages of Masha, Egor, and Anton. We can use the following equations to represent the given information:

1. The sum of their ages is 65: Masha + Egor + Anton = 65. 2. Egor is 7 years older than Masha: Egor = Masha + 7. 3. Egor is twice as old as Anton: Egor = 2 * Anton.

We can solve this system of equations to find the ages of each person.

Solving the Equations

Let's substitute the value of Egor from equation 3 into equation 2: Masha + 7 = 2 * Anton.

Now, let's substitute the value of Egor from equation 2 into equation 1: Masha + (Masha + 7) + Anton = 65.

Simplifying equation 1: 2 * Masha + Anton + 7 = 65.

Rearranging equation 1: 2 * Masha + Anton = 58.

Now, let's substitute the value of Egor from equation 3 into equation 1: 2 * Anton + Anton = 58.

Simplifying equation 1: 3 * Anton = 58.

Solving for Anton: Anton = 58 / 3.

Substituting the value of Anton into equation 3 to find Egor: Egor = 2 * (58 / 3).

Substituting the value of Egor into equation 2 to find Masha: Masha + 7 = 2 * (58 / 3).

Simplifying equation 2: Masha = (2 * (58 / 3)) - 7.

Now we can calculate the ages of each person.

Calculation

Using the equations above, we can calculate the ages of Masha, Egor, and Anton.

Masha = (2 * (58 / 3)) - 7. Egor = 2 * (58 / 3). Anton = 58 / 3.

Let's calculate the ages:

Masha = (2 * (58 / 3)) - 7 = 38. Egor = 2 * (58 / 3) = 38. Anton = 58 / 3 ≈ 19.33.

Answer

Based on the given information, the ages of Masha, Egor, and Anton are approximately: - Masha: 38 years - Egor: 38 years - Anton: 19.33 years.

Please note that Anton's age is approximate due to the division involved in the calculation.