Question

<<сколько лет твоему отцу?>> - Спросили Петю. Он ответил так: <<я втрое моложе папы, но я втрое старше сестры, а папе и сестре вместе 50 лет.>> сколько лет папе? Решить по действиям!!

Answer 1

To solve this problem, let's break down the information given:

- Petia said, "I am three times younger than my father, but I am three times older than my sister. My father and sister together are 50 years old."

Let's assign variables to the unknowns: - Let's call Petia's age "P". - Let's call Petia's father's age "F". - Let's call Petia's sister's age "S".

Based on the information given, we can create the following equations:

1. P = (1/3)F (Petia is three times younger than his father) 2. P = 3S (Petia is three times older than his sister) 3. F + S = 50 (The sum of Petia's father's age and his sister's age is 50)

Now, let's solve the equations to find the ages:

From equation 1, we can express F in terms of P: F = 3P

Substituting this value of F into equation 3, we get: 3P + S = 50

From equation 2, we can express S in terms of P: S = P/3

Substituting this value of S into the modified equation 3, we get: 3P + P/3 = 50

Multiplying through by 3 to eliminate the fraction, we get: 9P + P = 150

Combining like terms, we have: 10P = 150

Dividing both sides by 10, we find: P = 15

Now that we know Petia's age is 15, we can find the ages of his father and sister:

From equation 1, we have: F = 3P = 3 * 15 = 45

From equation 2, we have: S = P/3 = 15/3 = 5

Therefore, Petia's father is 45 years old.

To summarize: - Petia is 15 years old. - Petia's father is 45 years old. - Petia's sister is 5 years old.

I hope this helps! Let me know if you have any further questions.