Question

Возраст сестры сейчас составляет 3/4 возраста брата,а 8 лет назад брат был в 2 раза старше сестры.Сколько лет каждому сейчас?

Answer 1

 Возьмем теперешний возраст брата за Х.  Тогда сестре сейчас 3/4*Х. Тогда брату было Х-8, а сестре в два раза меньше (Х-8)/2 либо на восемь лет меньше, чем ей есть сейчас, т.е.  3/4*Х - 8. Приравняем эти два

(Х-8)/2 =  3/4*Х - 8

Умножим обе части на 2:

Х - 8 = 3/2*Х - 16

Перенесем Х в одну сторону, числа в другую:

16 - 8 = 3/2*Х - Х

Получим:

8 = 1/2*Х

Опять умножаем на два:

16 = Х

Значит, сейчас брату 16 лет, а сестре 12.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer 2

Problem Analysis

We are given that the current age of the sister is 3/4 of the brother's age, and 8 years ago the brother was twice as old as the sister. We need to find the current ages of both the sister and the brother.

Solution

Let's assume the current age of the brother is B years and the current age of the sister is S years.

From the given information, we can form two equations:

1. The current age of the sister is 3/4 of the brother's age: S = (3/4)B.

2. 8 years ago, the brother was twice as old as the sister: B - 8 = 2(S - 8).

Now, we can solve these two equations simultaneously to find the values of B and S.

Solving the Equations

Let's solve the equations using the substitution method.

From equation 1, we can express B in terms of S: B = (4/3)S.

Substituting this value of B into equation 2, we get:

(4/3)S - 8 = 2(S - 8).

Simplifying the equation:

(4/3)S - 8 = 2S - 16.

Multiplying through by 3 to eliminate the fraction:

4S - 24 = 6S - 48.

Bringing like terms to one side:

6S - 4S = 48 - 24.

2S = 24.

Dividing both sides by 2:

S = 12.

Now, we can substitute this value of S back into equation 1 to find B:

B = (4/3)S = (4/3)(12) = 16.

Answer

Therefore, the current age of the sister is 12 years and the current age of the brother is 16 years.