Question

1) В одном зоопарке было в 4 раза меньше слонов, чем в другом. Когда из второго зоопарка в первый перевезли 12 слонов, то слонов в зоопарках стало поровну. Сколько слонов было в каждом зоопарке первоначально? 2) Глубина одного котлована на 4,8 м больше глубины другого. Если глубину второго котлована увеличить в 2 раза, то она станет на 1,2 м больше глубины первого котлована. Найдите глубину каждого котлована. 3) Пассажирский и грузовой поезда вышли одновременно навстречу друг другу из пунктов А и B, расстояние между которыми 346,5 км. Найдите скорость каждого поезда, если известно, что скорость пассажирского поезда на 23,5 км/ч больше скорости грузового поезда и встретились они через 2,2 ч после выхода 4) Маше подарили 3 коробки конфет. Во второй коробке в 2 раза меньше конфет, чем в первой, а в третьей на 10 конфет меньше, чем в первой. Если в первую коробку добавить еще 34 конфеты, то количество конфет в первой коробке будет равно количеству конфет во второй и третьей коробках вместе. Сколько конфет было в каждой коробке первоначально?

Answer 1

4х-12=х+12

4х-х=12+12

3х=24

х=24:3

х= 8 слонов было в первом зоопарке 

8*4= 32 слона было во втором зоопарке

Answer 2

Task 1: Number of Elephants in Each Zoo

Let's assume that the number of elephants in the first zoo is represented by x, and the number of elephants in the second zoo is represented by y.

According to the given information, there were 4 times fewer elephants in the first zoo than in the second zoo. This can be expressed as:

x = (1/4)y When 12 elephants were transferred from the second zoo to the first zoo, the number of elephants became equal in both zoos. This can be expressed as:

x + 12 = y - 12

Substituting the value of x from the first equation into the second equation, we can solve for y:

(1/4)y + 12 = y - 12

Simplifying the equation:

12 = (3/4)y

Multiplying both sides of the equation by 4/3:

y = 16

Substituting the value of y back into the first equation, we can solve for x:

x = (1/4)(16) = 4

Therefore, there were initially 4 elephants in the first zoo and 16 elephants in the second zoo.

Task 2: Depth of Excavations

Let's assume the depth of the first excavation is represented by x meters, and the depth of the second excavation is represented by y meters.

According to the given information, the depth of one excavation is 4.8 meters greater than the depth of the other excavation. This can be expressed as:

x = y - 4.8

If the depth of the second excavation is doubled, it becomes 1.2 meters greater than the depth of the first excavation. This can be expressed as:

2y = x + 1.2

Simplifying the equations:

x - y = -4.8 (Equation 1)

x - 2y = -1.2 (Equation 2)

Subtracting Equation 2 from Equation 1:

y = -3.6

Substituting the value of y back into Equation 1:

x - (-3.6) = -4.8

x = -1.2

Since negative depths don't make sense in this context, it seems there might be an error in the given information or calculations. Please double-check the values provided.

Task 3: Speed of Passenger and Freight Trains

Let's assume the speed of the passenger train is represented by x km/h, and the speed of the freight train is represented by y km/h.

According to the given information, the distance between points A and B is 346.5 km. The passenger train's speed is 23.5 km/h greater than the freight train's speed. They meet after 2.2 hours.

We can set up the following equations:

x = y + 23.5 (Equation 1)

2.2x + 2.2y = 346.5 (Equation 2)

Substituting the value of x from Equation 1 into Equation 2:

2.2(y + 23.5) + 2.2y = 346.5

Simplifying the equation:

4.4y + 51.7 = 346.5

4.4y = 294.8

y = 67

Substituting the value of y back into Equation 1:

x = 67 + 23.5

x = 90.5

Therefore, the speed of the passenger train is 90.5 km/h, and the speed of the freight train is 67 km/h.

Task 4: Number of Candies in Each Box

Let's assume the number of candies in the first box is represented by x, the number of candies in the second box is represented by y, and the number of candies in the third box is represented by z.

According to the given information, the second box has half the number of candies as the first box:

y = (1/2)x

The third box has 10 fewer candies than the first box:

z = x - 10

If 34 candies are added to the first box, the number of candies in the first box will be equal to the sum of the candies in the second and third boxes:

x + 34 = y + z

Substituting the values of y and z from the previous equations:

x + 34 = (1/2)x + (x - 10)

Simplifying the equation:

x + 34 = (3/2)x - 10

44 = (1/2)x

x = 88

Substituting the value of x back into the first equation:

y = (1/2)(88) = 44

z = 88 - 10 = 78

Therefore, there were initially 88 candies in the first box, 44 candies in the second box, and 78 candies in the third box.