Question

маме,дочери и сыну вместе 37 лет.Известно,что мама на 22 года старше дочери,которая в 2 раза старше своего брата.Сколько лет дочери?

Answer 1

Problem Analysis

We are given that the sum of the ages of a mother, daughter, and son is 37 years. We also know that the mother is 22 years older than the daughter, and the daughter is twice as old as the son. We need to determine the age of the daughter.

Solution

Let's assume the age of the son is x years.

According to the given information, we can write the following equations:

1. Age of the mother + Age of the daughter + Age of the son = 37 2. Age of the mother = Age of the daughter + 22 3. Age of the daughter = 2 * Age of the son

We can solve this system of equations to find the age of the daughter.

Substituting equation 3 into equation 2, we get:

Age of the mother = 2 * Age of the son + 22

Substituting equation 3 into equation 1, we get:

2 * Age of the son + 22 + 2 * Age of the son + Age of the son = 37

Combining like terms, we have:

5 * Age of the son + 22 = 37

Subtracting 22 from both sides, we get:

5 * Age of the son = 15

Dividing both sides by 5, we get:

Age of the son = 3

Substituting the value of the son's age into equation 3, we get:

Age of the daughter = 2 * 3 = 6

Therefore, the age of the daughter is 6 years.

Answer

The age of the daughter is 6 years.