Question

Бабушка 6 лет назад была в 9 раз старше внучки. А 4 года назад в 7 раз старше внучки. Сколько лет бабушке и внучке.

Answer 1

Обозначим возраст бабушки через Б, а возраст внучки через в и составим систему уравнений по условию задачи
Б-6=9*(в-6)
Б-4=7*(в-4)
раскрываем скобки в правой части уравнений
Б-6=9в-54
Б-4=7в-28
и из первого уравнения вычитаем второе, получается
-2=2в-26
-2в=-26+2
-2в=-24
в=12 лет
подставляем найденный возраст внучки в любое уравнение системы и находим возраст бабушки
Б-6=9*(12-6)
Б-6=9*6
Б-6=54
Б=60 лет

Answer 2

Нужно так: х-6=9(у-6) -первое уравнение, х-4=7(у-4). Дальше Вы и сами справитесь. слева шестерку и четверку переносите в правую часть уравнения, затем уравниваете две правые части уравнения и у Вас получается у=12, х=60 - это возраст внучки и бабушки сейчас. соответственно, шесть лет назад было 6 и 54 (в 9 раз старше), а четыре года назад 8 и 56 (в 7 раз старше)

Answer 3

Problem Analysis

We are given two pieces of information about the age difference between a grandmother and her granddaughter. Six years ago, the grandmother was nine times older than the granddaughter, and four years ago, the grandmother was seven times older than the granddaughter. We need to determine the current ages of the grandmother and the granddaughter.

Solution

Let's assume the current age of the granddaughter is x years.

According to the first piece of information, six years ago, the grandmother was nine times older than the granddaughter. This can be represented as:

(grandmother's age six years ago) = 9 * (granddaughter's age six years ago)

The current age of the granddaughter is x years, so her age six years ago was x - 6 years. The current age of the grandmother is y years, so her age six years ago was y - 6 years.

Using this information, we can write the equation:

y - 6 = 9 * (x - 6)

According to the second piece of information, four years ago, the grandmother was seven times older than the granddaughter. This can be represented as:

(grandmother's age four years ago) = 7 * (granddaughter's age four years ago)

The age of the granddaughter four years ago was x - 4 years, and the age of the grandmother four years ago was y - 4 years.

Using this information, we can write the equation:

y - 4 = 7 * (x - 4)

We now have a system of two equations with two variables. We can solve this system of equations to find the values of x and y.

Solving the System of Equations

Let's solve the system of equations using the substitution method.

From the first equation, we can express y in terms of x:

y = 9 * (x - 6) + 6

Substituting this value of y into the second equation, we get:

9 * (x - 6) + 6 - 4 = 7 * (x - 4)

Simplifying the equation:

9 * (x - 6) + 2 = 7 * (x - 4)

Expanding and simplifying further:

9x - 54 + 2 = 7x - 28

Combining like terms:

9x - 52 = 7x - 28

Subtracting 7x from both sides:

2x - 52 = -28

Adding 52 to both sides:

2x = 24

Dividing both sides by 2:

x = 12

The current age of the granddaughter is 12 years.

Substituting this value of x into the first equation to find y:

y - 6 = 9 * (12 - 6)

Simplifying:

y - 6 = 9 * 6

y - 6 = 54

Adding 6 to both sides:

y = 60

The current age of the grandmother is 60 years.

Answer

The current age of the grandmother is 60 years, and the current age of the granddaughter is 12 years.