Question

На склад завезено три состава цистерны нефти.В первом составе 504т, во второй 288т ,а в третьей 648т нефти. Все цистерны заполнены нефтью и в каждой цистерне нефть одинаковой массы. Сколько тонн найбольшая вероятная масса нефти в каждой цистерне? Сколько цистерн в первом,втором и третьем составе?

Answer 1

Calculation of the Maximum Possible Mass of Oil in Each Tank

To calculate the maximum possible mass of oil in each tank, we need to find the common mass of oil in all three tanks. We can do this by finding the greatest common divisor (GCD) of the masses of oil in each tank.

The masses of oil in the three tanks are as follows: - First tank: 504 tons - Second tank: 288 tons - Third tank: 648 tons

To find the GCD, we can use the Euclidean algorithm. Let's calculate it step by step:

1. Find the GCD of 504 and 288: - GCD(504, 288) = GCD(288, 504 % 288) = GCD(288, 216) = GCD(216, 288 % 216) = GCD(216, 72) = GCD(72, 216 % 72) = GCD(72, 0) = 72

2. Find the GCD of 72 and 648: - GCD(72, 648) = GCD(648, 72 % 648) = GCD(648, 72) = GCD(72, 648 % 72) = GCD(72, 0) = 72

The GCD of 504, 288, and 648 is 72. Therefore, the maximum possible mass of oil in each tank is 72 tons.

Number of Tanks in Each Composition

Now let's determine the number of tanks in each composition.

- First composition: 504 tons of oil - Second composition: 288 tons of oil - Third composition: 648 tons of oil

Since the maximum possible mass of oil in each tank is 72 tons, we can divide the total mass of oil in each composition by 72 to find the number of tanks.

- Number of tanks in the first composition: 504 tons / 72 tons = 7 tanks - Number of tanks in the second composition: 288 tons / 72 tons = 4 tanks - Number of tanks in the third composition: 648 tons / 72 tons = 9 tanks

Therefore, there are 7 tanks in the first composition, 4 tanks in the second composition, and 9 tanks in the third composition.

Please note that these calculations assume that the tanks are filled to their maximum capacity and that the masses of oil in each tank are evenly distributed.