Question

Зерно на первом элеваторе составляет 70% зерна,имеющегося на втором элеваторе.Когда со второго элеватора вывезли 20% зерна,то на нем осталось на 200 т .зерна больше,чем было на первом.Сколько тонн зерна было на обоих элеваторах первоначально?

Answer 1

X - первоначальное кол-во зерна на 1-ом элеваторе
Y - первоначальное кол-во зерна на 2-ом элеваторе
(1) X = 0.7 * Y
(2) Y - 0.2Y = X+ 200
(1),(2) - система

0.8Y = 0.7Y+200 => Y = 2000, X = 1400
Ответ: 1400 -было на первом. 2000 - было на втором. На обоих: 3400

Answer 2

Problem Analysis

We are given that the grain on the first elevator constitutes 70% of the grain on the second elevator. When 20% of the grain is removed from the second elevator, there are 200 tons more grain left on the second elevator than there was on the first elevator initially. We need to determine the initial amount of grain on both elevators.

Solution

Let's assume that the initial amount of grain on the first elevator is x tons. Then, the initial amount of grain on the second elevator would be 0.7x tons, since it constitutes 70% of the grain on the second elevator.

When 20% of the grain is removed from the second elevator, there are 200 tons more grain left on the second elevator than there was on the first elevator initially. This can be expressed as the equation:

0.8(0.7x) = x + 200

Let's solve this equation to find the value of x.

Calculation

Simplifying the equation:

0.56x = x + 200

0.56x - x = 200

-0.44x = 200

Dividing both sides by -0.44:

x = -200 / -0.44

x = 454.55

Therefore, the initial amount of grain on the first elevator was approximately 454.55 tons.

To find the initial amount of grain on the second elevator, we can substitute this value back into the equation:

0.7x = 0.7 * 454.55

x = 318.18

Therefore, the initial amount of grain on the second elevator was approximately 318.18 tons.

Answer

The initial amount of grain on both elevators was approximately 454.55 tons on the first elevator and 318.18 tons on the second elevator.