Question

Тане с Сашей вместе 14 лет, Саше с Петей 20 лет, а Тане с Петей 16 лет. Сколько лет каждому из них?

Answer 1

Им всем вместе 25 лет. При чем Саше и Пете вместе 20 лет, значит, Тане 5 лет.
Тане и Саше вместе 14 лет, значит, Саше 9 лет
Саше и Пете вместе 20 лет, значит, Пете 11 лет

Answer 2

Calculation of Ages

To determine the ages of Tanja, Sasha, and Petya, we can use the given information. Let's break it down:

- Tanja and Sasha have been together for 14 years. - Sasha and Petya have been together for 20 years. - Tanja and Petya have been together for 16 years.

To calculate their ages, we can set up a system of equations based on the given information:

1. Tanja's age + Sasha's age = 14 years 2. Sasha's age + Petya's age = 20 years 3. Tanja's age + Petya's age = 16 years

Let's solve this system of equations to find the ages of each person.

Solution

To solve the system of equations, we can use substitution or elimination. Let's use the elimination method:

From equations 1 and 2, we can subtract equation 1 from equation 2 to eliminate Sasha's age:

(Sasha's age + Petya's age) - (Tanja's age + Sasha's age) = 20 years - 14 years

Simplifying, we get:

Petya's age - Tanja's age = 6 years

Now, we have two equations:

1. Petya's age - Tanja's age = 6 years 2. Tanja's age + Petya's age = 16 years

Adding equations 1 and 3, we can eliminate Tanja's age:

(Petya's age - Tanja's age) + (Tanja's age + Petya's age) = 6 years + 16 years

Simplifying, we get:

2 * Petya's age = 22 years

Dividing both sides by 2, we find:

Petya's age = 11 years

Substituting Petya's age back into equation 3, we can find Tanja's age:

Tanja's age + 11 years = 16 years

Subtracting 11 years from both sides, we get:

Tanja's age = 5 years

Finally, we can substitute Petya's age and Tanja's age into equation 1 to find Sasha's age:

Sasha's age = 14 years - Tanja's age

Substituting Tanja's age, we get:

Sasha's age = 14 years - 5 years

Simplifying, we find:

Sasha's age = 9 years

Conclusion

Based on the given information, we can determine the ages of each person:

- Tanja is 5 years old. - Sasha is 9 years old. - Petya is 11 years old.

Please note that these calculations are based on the information provided and assume that the ages are accurate.