Question

Маша старше Серёжи на 3 года, а маме в 2 раза больше лет, чем Маше и Сереже вместе взятым. Всем вместе им 45 лет. Сколько лет каждому?

Answer 1

Серёже 6 лет, Маше 9 лет, Маме 30 лет

Answer 2

Problem Analysis

We are given the following information: - Masha is 3 years older than Sergey. - The mother is twice as old as Masha and Sergey combined. - The sum of their ages is 45 years.

We need to determine the age of each person.

Solution

Let's assign variables to the ages of Masha, Sergey, and the mother: - Let's denote Masha's age as M. - Sergey's age will be denoted as S. - The mother's age will be denoted as Mm.

We can set up the following equations based on the given information: 1. Masha is 3 years older than Sergey: M = S + 3. 2. The mother is twice as old as Masha and Sergey combined: Mm = 2(M + S). 3. The sum of their ages is 45 years: M + S + Mm = 45.

We can solve this system of equations to find the values of M, S, and Mm.

Solving the Equations

Let's substitute equation 1 into equation 2 to eliminate M: Mm = 2((S + 3) + S) = 2(2S + 3) = 4S + 6.

Now we can substitute the value of Mm from equation 2 into equation 3: S + (S + 3) + (4S + 6) = 45.

Simplifying the equation: 6S + 9 = 45.

Subtracting 9 from both sides: 6S = 36.

Dividing both sides by 6: S = 6.

Now we can substitute the value of S into equation 1 to find M: M = 6 + 3 = 9.

Finally, we can substitute the values of M and S into equation 2 to find Mm: Mm = 2(9 + 6) = 2(15) = 30.

Answer

Therefore, Masha is 9 years old, Sergey is 6 years old, and their mother is 30 years old.