Question

СРОЧНО Вместимость первого ведра составляет два на 2/3 вместимости второго, а вместимость второго ведра составляет 3/4 вместимости третьего. В каждом из вёдер налита вода: в первом ведре-половина его вместимости, во втором – 3/7 вместимости, а в третьем – 1/14 вместимости. Всего в трёх вёдрах 18 л воды. Какова вместимость второго ведра (в литрах)?

Answer 1

Ответ 19 нщдрсндпгзпнщсщесрдчп

Answer 2

Ответ:

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Answer 3

Problem Analysis

To solve this problem, we need to determine the capacity of the second bucket in liters. We are given the following information: - The capacity of the first bucket is 2/3 of the capacity of the second bucket. - The capacity of the second bucket is 3/4 of the capacity of the third bucket. - The first bucket is filled to half of its capacity. - The second bucket is filled to 3/7 of its capacity. - The third bucket is filled to 1/14 of its capacity. - The total amount of water in the three buckets is 18 liters.

Solution

Let's assume the capacity of the third bucket is x liters.

According to the given information: - The capacity of the second bucket is 3/4 of x, which is (3/4)x liters. - The capacity of the first bucket is 2/3 of (3/4)x, which is (2/3)(3/4)x liters.

We are also given the following information about the amount of water in each bucket: - The first bucket is filled to half of its capacity, which is (1/2)(2/3)(3/4)x liters. - The second bucket is filled to 3/7 of its capacity, which is (3/7)(3/4)x liters. - The third bucket is filled to 1/14 of its capacity, which is (1/14)x liters.

The total amount of water in the three buckets is 18 liters, so we can set up the following equation:

(1/2)(2/3)(3/4)x + (3/7)(3/4)x + (1/14)x = 18

Now, let's solve this equation to find the value of x, which represents the capacity of the third bucket.

Calculation

To solve the equation, we can follow these steps:

Step 1: Simplify the equation by multiplying the fractions: (1/2)(2/3)(3/4)x + (3/7)(3/4)x + (1/14)x = 18 (1/3)(3/4)x + (9/28)x + (1/14)x = 18

Step 2: Find a common denominator for the fractions: (7/7)(1/3)(3/4)x + (6/6)(9/28)x + (2/2)(1/14)x = 18 (7/12)x + (54/168)x + (1/14)x = 18

Step 3: Combine like terms: (7/12 + 54/168 + 1/14)x = 18 (98/168 + 54/168 + 12/168)x = 18 (164/168)x = 18

Step 4: Solve for x: (164/168)x = 18 x = (18 * 168)/164 x ≈ 18.54

The capacity of the third bucket is approximately 18.54 liters.

Answer

The capacity of the second bucket is 3/4 of the capacity of the third bucket, which is approximately (3/4) * 18.54 ≈ 13.91 liters. Therefore, the capacity of the second bucket is approximately 13.91 liters.