Question

Решить задачу: В ботаническом саду живут попугай, ласточка, аист и 4 журавля. Сумма возрастов одного журавля и ласточки- 25 лет, аиста и ласточки-18 лет, при этом возраст аиста равен 2/3 возраста журавля. Чему равна сумма возрастов всех птиц, живущих в саду, если возраст попугая равен утроенной сумме возрастов всех остальных птиц, а все журавли одного возраста.

Answer 1

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Answer 2

Problem Analysis

We are given the ages of different birds in a botanical garden: a parrot, a swallow, a stork, and four cranes. We are also given some information about the sums of ages between certain pairs of birds. We need to find the sum of ages of all the birds in the garden.

Let's assign variables to the ages of each bird: - Let's denote the age of the parrot as P. - Let's denote the age of the swallow as S. - Let's denote the age of the stork as A. - Let's denote the age of each crane as C.

We are given the following information: 1. The sum of ages between one crane and the swallow is 25 years: C + S = 25. 2. The sum of ages between the stork and the swallow is 18 years: A + S = 18. 3. The age of the stork is 2/3 of the age of a crane: A = (2/3)C. 4. The age of the parrot is three times the sum of ages of all the other birds: P = 3(S + A + 4C). 5. All the cranes have the same age: C1 = C2 = C3 = C4.

We need to find the sum of ages of all the birds in the garden: P + S + A + 4C.

Solving the Problem

Let's solve the system of equations using the given information.

From equation 3, we can express the age of the stork in terms of the age of a crane: A = (2/3)C.

Substituting this value of A into equation 2, we get: (2/3)C + S = 18.

Simplifying this equation, we get: 2C + 3S = 54. (Equation 5)

From equation 1, we can express the age of the swallow in terms of the age of a crane: S = 25 - C.

Substituting this value of S into equation 5, we get: 2C + 3(25 - C) = 54.

Simplifying this equation, we get: 2C + 75 - 3C = 54.

Simplifying further, we get: C = 21.

Now that we know the age of a crane, we can find the age of the stork using equation 3: A = (2/3)C = (2/3)(21) = 14.

Using the age of the stork, we can find the age of the swallow using equation 2: S = 18 - A = 18 - 14 = 4.

Finally, we can find the age of the parrot using equation 4: P = 3(S + A + 4C) = 3(4 + 14 + 4(21)) = 3(4 + 14 + 84) = 3(102) = 306.

Now we can find the sum of ages of all the birds in the garden: P + S + A + 4C = 306 + 4 + 14 + 4(21) = 306 + 4 + 14 + 84 = 408.

Therefore, the sum of ages of all the birds in the garden is 408 years.

Answer

The sum of ages of all the birds living in the botanical garden is 408 years.

Note: The solution provided above is based on the given information and the calculations made using that information.