Question

Пони пригласили в гости в школу в 4-й класс школы №2018.В этом классе 25 учеников,причем у них бывает всего три имени:Маша,Миша и Саша.Оказалось, что учеников по имени Маша вдвое меньше,чем всех девочек.Кроме того,учеников по имени Миша втрое меньше,чем всех мальчиков.И,наконецучеников по имени Миша столько же, сколько же,сколько учеников по имени Маша. Сколько мальчиков и сколько девочек в 4-м классе школы №2018?

Answer 1

Ответ:

10 девочек, 15 мальчиков

Пошаговое объяснение:

Маша - только девочки, Миша - только мальчики, Саша - как девочки, так и мальчики.

Маша - 1/2 девочек, Миша - 1/3 мальчиков, и они равны.

Возьмём за х- количество Маш, тогда всех девочек 2х (т.к. 1/2 девочек =х) а всех мальчиков 3х (т.к. 1/3 мальчиков =х). Девочек и мальчиков в сумме 5х, что по условию задачи 25

5х=25

х=5.

Тогда девочек 2*5 = 10, а мальчиков 3*5 = 15.

Answer 2

Problem Analysis

We are given that there are 25 students in the 4th grade of School #2018, and they have only three names: Masha, Misha, and Sasha. It is also mentioned that the number of students named Masha is half the number of all girls, the number of students named Misha is one-third the number of all boys, and the number of students named Misha is the same as the number of students named Masha. We need to determine the number of boys and girls in the 4th grade.

Solution

Let's assume the number of students named Masha is x. According to the given information, the number of students named Misha is also x.

We can set up the following equations based on the given information: 1. The number of students named Masha is half the number of all girls: x = (1/2) * (number of girls) 2. The number of students named Misha is one-third the number of all boys: x = (1/3) * (number of boys) 3. The number of students named Misha is the same as the number of students named Masha: x = x

To solve this system of equations, we can substitute the value of x from equation 3 into equations 1 and 2.

Solution Steps:

1. Substitute the value of x from equation 3 into equations 1 and 2: - Equation 1: x = (1/2) * (number of girls) - Equation 2: x = (1/3) * (number of boys) 2. Substitute the value of x from equation 3 into equations 1 and 2: - Equation 1: x = (1/2) * (number of girls) - Equation 2: x = (1/3) * (number of boys) 3. Equate the right-hand sides of equations 1 and 2: - (1/2) * (number of girls) = (1/3) * (number of boys) 4. Solve the equation for the number of girls: - (1/2) * (number of girls) = (1/3) * (number of boys) - Multiply both sides by 2: number of girls = (2/3) * (number of boys) 5. Substitute the value of the number of girls into equation 1 to solve for x: - x = (1/2) * (number of girls) - Substitute the value of the number of girls: x = (1/2) * [(2/3) * (number of boys)] - Simplify: x = (1/3) * (number of boys) 6. Equate the two expressions for x: - x = (1/3) * (number of boys) - x = x 7. Solve for the number of boys: - Equate the two expressions for x: (1/3) * (number of boys) = x - Substitute the value of x from equation 3: (1/3) * (number of boys) = x = (1/3) * (number of boys) - Multiply both sides by 3: number of boys = number of boys - The number of boys can be any positive integer.

Therefore, we cannot determine the exact number of boys and girls in the 4th grade of School #2018 based on the given information. The number of boys can be any positive integer, and the number of girls will be (2/3) times the number of boys.

Please let me know if I can help you with anything else.