Question

16. В двух группах детского сада было 50 детей. Когда число детей средней группы уменьшили на 20%, а в младшей увеличили на 40%, то в средней группе стало на 4 ребенка меньше, чем в младшей. Сколько детей было в каждой группе первоначально?

Answer 1

Ответ:30,20

Объяснение:

20%*5=100%, 4*5 =20 детей - в первой

50 - 20= 30 - во второй

Answer 2

Ответ:

20, и 30 детей

Объяснение:

Смотри, если 4 ребёнка это 20 %, то 20%*5=100% то есть 4*5 =20 детей - в первой

Все очень просто

50 - 20= 30 - во второй

Answer 3

Problem Analysis

We are given two groups in a kindergarten, and the total number of children in both groups is 50. After decreasing the number of children in the middle group by 20% and increasing the number of children in the younger group by 40%, the middle group has 4 fewer children than the younger group. We need to determine the initial number of children in each group.

Solution

Let's assume the initial number of children in the middle group is x and the initial number of children in the younger group is y.

According to the problem, the total number of children in both groups is 50, so we can write the equation:

x + y = 50 ---(1)

After decreasing the number of children in the middle group by 20%, the new number of children in the middle group is 80% of the initial number, which can be expressed as 0.8x.

After increasing the number of children in the younger group by 40%, the new number of children in the younger group is 140% of the initial number, which can be expressed as 1.4y.

According to the problem, the middle group has 4 fewer children than the younger group, so we can write the equation:

0.8x = 1.4y - 4 ---(2)

Now we have a system of two equations (equations 1 and 2) with two variables (x and y). We can solve this system of equations to find the values of x and y.

Solving the System of Equations

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

From equation 1, we can express x in terms of y:

x = 50 - y

Substituting this value of x into equation 2, we get:

0.8(50 - y) = 1.4y - 4

Simplifying the equation:

40 - 0.8y = 1.4y - 4

Adding 0.8y to both sides:

40 = 2.2y - 4

Adding 4 to both sides:

44 = 2.2y

Dividing both sides by 2.2:

y = 20

Substituting this value of y into equation 1, we get:

x + 20 = 50

Subtracting 20 from both sides:

x = 30

Therefore, the initial number of children in the middle group was 30 and the initial number of children in the younger group was 20.

Answer

The initial number of children in each group was 30 in the middle group and 20 in the younger group.