Question

В одной цистерне в 4 раза меньше нефти чем во второй . после того как в первую цистерну добавили 20т нефти , а из второй откачали 19т нефти в обеих цистернах стало поровну . сколько тонн нефти в каждой цистерне первоночально ?

Answer 1

Пусть в первой цистерне будет х т. Нефти, тогда во второй будет 4 х, х+20 будет нефти после 20 т. Добавления, во второй будет после откачки 19 т.(4х-19), составляем уравнение х+20=4х-19, находим х,х-4х=-20-19,-3х=-39, меняем знаки, х=13(в первой цистерне первоначально),4*13=52( первоначально во 2)

Answer 2

Problem Analysis

We have two tanks, and the amount of oil in the first tank is 4 times less than the amount of oil in the second tank. After adding 20 tons of oil to the first tank and removing 19 tons of oil from the second tank, the amount of oil in both tanks becomes equal. We need to find the initial amount of oil in each tank.

Solution

Let's assume the initial amount of oil in the second tank is x tons. Since the amount of oil in the first tank is 4 times less than the amount in the second tank, the initial amount of oil in the first tank is x/4 tons.

After adding 20 tons of oil to the first tank, the amount of oil in the first tank becomes (x/4) + 20 tons. After removing 19 tons of oil from the second tank, the amount of oil in the second tank becomes x - 19 tons.

According to the problem, the amount of oil in both tanks becomes equal. Therefore, we can set up the following equation:

(x/4) + 20 = x - 19

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

Equation Solving

(x/4) + 20 = x - 19

Multiply both sides of the equation by 4 to eliminate the fraction:

x + 80 = 4x - 76

Subtract x from both sides:

80 = 3x - 76

Add 76 to both sides:

156 = 3x

Divide both sides by 3:

x = 52

Answer

The initial amount of oil in the second tank is 52 tons. Since the amount of oil in the first tank is 4 times less than the amount in the second tank, the initial amount of oil in the first tank is 52/4 = 13 tons.

Therefore, the initial amount of oil in each tank is 13 tons in the first tank and 52 tons in the second tank.

Answer 3

Problem Analysis

We are given two tanks, and initially, the first tank contains four times less oil than the second tank. After adding 20 tons of oil to the first tank and removing 19 tons of oil from the second tank, the amount of oil in both tanks becomes equal. We need to find the initial amount of oil in each tank.

Solution

Let's assume the initial amount of oil in the first tank is x tons. Then the initial amount of oil in the second tank would be 4x tons, as stated in the problem.

After adding 20 tons of oil to the first tank, the amount of oil in the first tank becomes x + 20 tons. And after removing 19 tons of oil from the second tank, the amount of oil in the second tank becomes 4x - 19 tons.

According to the problem, the amount of oil in both tanks becomes equal. So we can set up the following equation:

x + 20 = 4x - 19

Now we can solve this equation to find the value of x.

Solving the Equation

Let's solve the equation step by step:

x + 20 = 4x - 19

First, let's move all the terms containing x to one side of the equation:

x - 4x = -19 - 20

Simplifying the equation:

-3x = -39

Dividing both sides of the equation by -3:

x = 13

So the initial amount of oil in the first tank is 13 tons.

Since the initial amount of oil in the second tank is four times less than the first tank, the initial amount of oil in the second tank is:

4x = 4 * 13 = 52 tons.

Therefore, the initial amount of oil in each tank is 13 tons in the first tank and 52 tons in the second tank.

Answer

The initial amount of oil in each tank is 13 tons in the first tank and 52 tons in the second tank.

Verification

Let's verify our answer by substituting the values back into the original equation:

Initial amount of oil in the first tank = 13 tons Initial amount of oil in the second tank = 52 tons

After adding 20 tons of oil to the first tank: 13 + 20 = 33 tons After removing 19 tons of oil from the second tank: 52 - 19 = 33 tons

The amount of oil in both tanks is now equal, which confirms our answer.