Question

На двух кустах сидели 25 снегирей. Когда с первого куста перелетели на второй 5 снегирей, а со второго 7 снегирей улетело, то на первом кусте осталось птиц в 2 раза больше, чем на втором. Сколько птиц было на каждом кусте первоначально?

Answer 1

Х - на первом кусте, 25-х  - на втором кусте
х-5 =2*((25-х)+5-7)
х-5=2*(23-х)
х-5=46-2х
3х=51
х=17 - на первом кусте
25-17=8 - на втором кусте

Answer 2

Problem Analysis

We are given that there were 25 bullfinches sitting on two bushes. When 5 bullfinches flew from the first bush to the second bush, and 7 bullfinches flew from the second bush, the number of bullfinches on the first bush was twice the number on the second bush. We need to determine the initial number of bullfinches on each bush.

Solution

Let's assume that the initial number of bullfinches on the first bush is x and on the second bush is y.

According to the given information: - When 5 bullfinches flew from the first bush to the second bush, the number of bullfinches on the first bush decreased by 5: x - 5. - When 7 bullfinches flew from the second bush, the number of bullfinches on the second bush decreased by 7: y - 7. - The number of bullfinches on the first bush after the transfers is twice the number on the second bush: x - 5 = 2(y - 7).

We can now solve this equation to find the values of x and y.

Solving the Equation

Let's solve the equation x - 5 = 2(y - 7) for x and y.

Expanding the equation: x - 5 = 2y - 14

Rearranging the equation: x - 2y = -9

Now we have a system of two equations: x - 2y = -9 (Equation 1) x + y = 25 (Equation 2)

We can solve this system of equations using substitution or elimination.

Using the substitution method, we can solve Equation 2 for x and substitute it into Equation 1.

From Equation 2, we have: x = 25 - y

Substituting this value of x into Equation 1: 25 - y - 2y = -9

Simplifying the equation: -3y = -34

Dividing both sides by -3: y = 34/3

Substituting this value of y back into Equation 2 to find x: x + 34/3 = 25

Simplifying the equation: x = 25 - 34/3

Converting the mixed number to an improper fraction: x = 75/3 - 34/3

Simplifying the equation: x = 41/3

Therefore, the initial number of bullfinches on the first bush (x) is 41/3, and the initial number of bullfinches on the second bush (y) is 34/3.

Answer

The initial number of bullfinches on each bush was: - First bush: 41/3 (approximately 13.67) bullfinches. - Second bush: 34/3 (approximately 11.33) bullfinches.