Question

Рядом стоят две бочки. Когда из одной взяли 7 ведер воды, а в другую налили 3 ведра воды, то в обоих бочках воды стало поровну. На сколько ведер воды водной из бочек было больше, чем в другой? Как записать краткое пояснение????

Answer 1

Problem Analysis

We have two barrels, and 7 buckets of water are taken from one barrel and poured into the other barrel, resulting in an equal amount of water in both barrels. We need to determine how many more buckets of water were in one barrel compared to the other.

Solution

Let's assume that the initial amount of water in the first barrel is x buckets, and the initial amount of water in the second barrel is y buckets.

After taking 7 buckets of water from the first barrel, the amount of water in the first barrel becomes x - 7, and after pouring 3 buckets of water into the second barrel, the amount of water in the second barrel becomes y + 3.

According to the problem statement, the amount of water in both barrels is equal after these operations. Therefore, we can set up the following equation:

x - 7 = y + 3

To find the difference in the amount of water between the two barrels, we need to find the value of (x - y).

Let's solve the equation to find the value of (x - y).

Equation Solution

Starting with the equation x - 7 = y + 3, we can isolate (x - y) by adding y to both sides of the equation:

x - 7 + y = y + 3 + y

Simplifying the equation:

x - y - 7 = 3 + 2y

Next, we can add 7 to both sides of the equation:

x - y - 7 + 7 = 3 + 2y + 7

Simplifying the equation further:

x - y = 10 + 2y

Finally, we can subtract 2y from both sides of the equation:

x - y - 2y = 10 + 2y - 2y

Simplifying the equation one last time:

x - 3y = 10

Therefore, the difference in the amount of water between the two barrels is x - y = 10 buckets.

Conclusion

The amount of water in one barrel was 10 buckets more than the amount of water in the other barrel.

Please let me know if anything is unclear or if you have any further questions!