Question

Реши задачу алгебраически:,,Сколько лет твоему отцу?"-спросили у Пети.Он ответил ,,Я втрое моложе папы,но зато втрое старше своей сестры,а папе и сестре вместе 50 лет".Сколько лет отцу?

Answer 1

Пусть x возраст мальчика тогда возрост сестры x/3 а отца x*3 составляем уравнение

3х+х/3=50

9х+х=50*3

10x=150

x=15

(15 лет пете)

15*3=45 (лет отцу)

Ответ:45 лет

Answer 2

Problem Analysis

To solve this problem algebraically, we need to set up equations based on the given information and then solve for the unknown variable, which is the age of the father.

Given Information

1. Peti is three times younger than his father. 2. Peti is three times older than his sister. 3. The sum of the ages of Peti's father and sister is 50 years.

Let's set up the equations:

Let's assume the age of Peti's father is F years, Peti's age is P years, and his sister's age is S years.

From the given information, we can write the following equations: 1. P = (1/3)F (Peti is three times younger than his father) 2. P = 3S (Peti is three times older than his sister) 3. F + S = 50 (The sum of the ages of Peti's father and sister is 50 years)

Solving the Equations

To solve these equations, we can substitute the value of P from equation 1 into equation 2: (1/3)F = 3S

Now, we can substitute the value of S from equation 3 into the above equation: (1/3)F = 3(50 - F)

Simplifying the equation: (1/3)F = 150 - 3F

Multiplying both sides of the equation by 3 to eliminate the fraction: F = 450 - 9F

Adding 9F to both sides of the equation: 10F = 450

Dividing both sides of the equation by 10: F = 45

Therefore, the age of Peti's father is 45 years.

Answer

The age of Peti's father is 45 years.

Note: The solution to this problem is based on the given information and the assumption that the ages are whole numbers.