Question

Мать старше дочери на 24 года, а через 5 лет будет старше ее в 5 раз. Сколько лет матери и сколько лет дочери?

Answer 1

Пусть дочке х лет, тогда маме х+24 года.

Через 5 летмаме будет х+29 лет, а дочке х+5 лет и мама будет старше в пять раз

Решим уравнение:

х+29=5*(х+5)

4x=4

x=1

 

Ответ: 25, 1

Answer 2

Problem Analysis

We are given that a mother is 24 years older than her daughter, and in 5 years, the mother will be 5 times older than her daughter. We need to determine the ages of the mother and the daughter.

Solution

Let's assume the current age of the daughter is x years. According to the given information, the current age of the mother is x + 24 years.

In 5 years, the daughter's age will be x + 5 years, and the mother's age will be x + 24 + 5 years.

According to the second part of the information, the mother's age in 5 years will be 5 times the daughter's age in 5 years. Mathematically, we can represent this as:

x + 24 + 5 = 5(x + 5)

Now, let's solve this equation to find the value of x.

x + 24 + 5 = 5x + 25

Simplifying the equation:

24 + 5 = 5x - x + 25

29 = 4x + 25

4x = 29 - 25

4x = 4

x = 1

Therefore, the current age of the daughter is 1 year.

To find the current age of the mother, we substitute the value of x into the equation:

Mother's age = x + 24 = 1 + 24 = 25

So, the current age of the mother is 25 years, and the current age of the daughter is 1 year.

Answer

The current age of the mother is 25 years, and the current age of the daughter is 1 year.