Question

Построй математическую модель задачи и реши ее Возраст младшей сестры на 5 лет меньше возраста средней и в 5 раз меньше старшей . Сколько лет каждой девочке если вместе им 19???????????!!!!

Answer 1

Возмём возраст младшей сестры за Х, тогда возраст средней сестры х+5, а возраст старшей сестры 5х.А их возраст в сумме даёт 19 лет
Сост. Уравн.:
х+х+5+5х=19
7х=19-5
7х=14
х=14/7
х=2(года)-младшей сестре
5+2=7(лет)-средней сестре
5*2=10(лет)-старшей сестре

Answer 2

Mathematical Model and Solution

To solve the problem, let's assign variables to represent the ages of the three sisters. Let's call the age of the youngest sister "y," the age of the middle sister "m," and the age of the oldest sister "o."

According to the problem statement, the age of the youngest sister is 5 years less than the age of the middle sister. So we can write the equation: y = m - 5.

The age of the youngest sister is also 5 times less than the age of the oldest sister. So we can write the equation: y = o / 5.

We also know that the sum of their ages is 19. So we can write the equation: y + m + o = 19.

Now we have a system of three equations with three variables. We can solve this system to find the ages of the three sisters.

Substituting the first equation into the second equation, we get: m - 5 = o / 5.

Rearranging this equation, we get: 5m - 25 = o.

Substituting this equation into the third equation, we get: y + m + 5m - 25 = 19.

Combining like terms, we get: 6m + y = 44.

Now we have two equations with two variables. We can substitute the value of "y" from the first equation into the second equation to solve for "m."

Substituting y = m - 5 into 6m + y = 44, we get: 6m + (m - 5) = 44.

Simplifying this equation, we get: 7m - 5 = 44.

Adding 5 to both sides of the equation, we get: 7m = 49.

Dividing both sides of the equation by 7, we get: m = 7.

Now that we have the value of "m," we can substitute it back into the first equation to find the value of "y."

Substituting m = 7 into y = m - 5, we get: y = 7 - 5 = 2.

Finally, we can substitute the values of "y" and "m" into the third equation to find the value of "o."

Substituting y = 2 and m = 7 into y + m + o = 19, we get: 2 + 7 + o = 19.

Simplifying this equation, we get: o = 19 - 2 - 7 = 10.

Therefore, the ages of the three sisters are: - The youngest sister is 2 years old. - The middle sister is 7 years old. - The oldest sister is 10 years old.

Please note that the solution to this problem is based on the given information and the mathematical model we constructed.