Question

Возраст мальчика и девочки в сумме составляет 20 лет. Через 4 года возраст девочки будет в три раза больше возраста мальчика. Сколько лет будет каждому из них через 2 года? С решением пожалуйста!​

Answer 1

Ответ:

5 и 19

Пошаговое объяснение:

Тут можно методом подбора

Допустим что мальчику 3 года, а девочке 17 лет

И через 4 года им будет по 7 и 21 лет, по условию подходят, девочка старше в 3 раза.

Значит через 2 года им будет :

Мальчику 5 лет

Девочке 19 лет

Answer 2

Problem Analysis

We are given that the sum of the ages of a boy and a girl is 20 years. After 4 years, the girl's age will be three times the boy's age. We need to determine the ages of both the boy and the girl after 2 years.

Let's assume the current age of the boy is B years and the current age of the girl is G years. We can set up the following equations based on the given information:

1. B + G = 20 (The sum of their ages is 20) 2. G + 4 = 3(B + 4) (After 4 years, the girl's age will be three times the boy's age)

We can solve these equations to find the values of B and G.

Solving the Equations

Let's solve the equations to find the ages of the boy and the girl.

From equation 1, we have B + G = 20. We can rewrite this equation as G = 20 - B.

Substituting G = 20 - B into equation 2, we get (20 - B) + 4 = 3(B + 4).

Simplifying the equation, we have 24 - B = 3B + 12.

Combining like terms, we get 4B = 12.

Dividing both sides by 4, we find B = 3.

Substituting B = 3 into equation 1, we have 3 + G = 20.

Simplifying the equation, we find G = 17.

Therefore, the current age of the boy is 3 years and the current age of the girl is 17 years.

Ages after 2 Years

To find the ages of the boy and the girl after 2 years, we simply add 2 to their current ages.

The boy's age after 2 years will be 3 + 2 = 5 years.

The girl's age after 2 years will be 17 + 2 = 19 years.

Therefore, after 2 years, the boy will be 5 years old and the girl will be 19 years old.

Answer: The boy will be 5 years old and the girl will be 19 years old after 2 years.

Verification

Let's verify our solution by checking if the given conditions are satisfied.

1. The sum of their ages is 20: 3 + 17 = 20 (satisfied). 2. After 4 years, the girl's age will be three times the boy's age: (17 + 4) = 3(3 + 4) => 21 = 21 (satisfied).

Therefore, our solution is correct.