Question

Из полной бочки отлили 2\5 воды, потом 1\3 оставшейся в ней воды, после чего в бочке осталось 8 ведер. Сколько воды было в бочке первоначально?

Answer 1

1-2/5=3/5 осталось после первого отлива

1/3*3/5=1/5 отлили второй раз

1-(3/5+1/5)=1/5 - осталось

8*5=40 ведер воды было в бочке

Answer 2

Problem Analysis

We are given that 2/5 of the water was poured out of a barrel, then 1/3 of the remaining water was poured out, leaving 8 buckets of water in the barrel. We need to determine the initial amount of water in the barrel.

Solution

Let's assume that the initial amount of water in the barrel is represented by the variable x.

According to the problem, 2/5 of the water was poured out, leaving 3/5 of the water in the barrel. This can be represented as:

(3/5) * x

Then, 1/3 of the remaining water was poured out, leaving 2/3 of the water in the barrel. This can be represented as:

(2/3) * (3/5) * x

Finally, we are given that there are 8 buckets of water left in the barrel. We can set up the equation:

(2/3) * (3/5) * x = 8

To find the initial amount of water in the barrel, we can solve this equation for x.

Calculation

Let's solve the equation:

(2/3) * (3/5) * x = 8

Simplifying the equation:

(2/3) * (3/5) * x = 8 (2/5) * x = 8

Multiplying both sides by 5/2 to isolate x:

x = (8 * 5/2) / (2/5) x = (40/2) / (2/5) x = 20 / (2/5) x = 20 * (5/2) x = 100/2 x = 50

Answer

The initial amount of water in the barrel was 50 units.

Explanation

Initially, the barrel contained 50 units of water. 2/5 of the water was poured out, leaving 30 units of water in the barrel. Then, 1/3 of the remaining water was poured out, leaving 20 units of water in the barrel. Finally, 8 buckets of water were left in the barrel, which confirms our calculation.