Question

В мешке имеется 9 кг сахара. Есть также и две гири по 50 г и 200 г. Подумайте, как за 3 взвешивания на чашечных весах отвесить 2 кг сахара?

Answer 1

Первое взвешивание: уравнять на одной чаше весов 4,4 кг+гиря, а на другой - 4,6 кг 
Второе взвешивание: взять пакет с 4,4 кг и разделить его на весах пополам - по 2,2 кг. 
Третье взвешивание: отвесить и пакета весом 2,2 кг ровно 200 грамм, уравняв это количество сахара с гирей. 

Answer 2

Problem Analysis

To weigh 2 kg of sugar using the given 9 kg of sugar and two weights of 50 g and 200 g, we need to come up with a strategy that allows us to determine the weight of the sugar accurately using only three weighings on a balance scale.

Solution

Here's a step-by-step solution to the problem:

1. First Weighing: - Place one 50 g weight on one side of the balance scale and 100 g of sugar on the other side. - If the scale balances, then the weight of the sugar is 100 g. - If the scale does not balance, move to the next step.

2. Second Weighing: - Remove the 50 g weight from the balance scale. - Divide the remaining 100 g of sugar into two equal parts, each weighing 50 g. - Place one of the 50 g sugar portions on one side of the balance scale and the other 50 g sugar portion on the other side. - If the scale balances, then the weight of the sugar is 150 g (100 g from the first weighing + 50 g from the second weighing). - If the scale does not balance, move to the next step.

3. Third Weighing: - Remove the 50 g sugar portion from the balance scale. - Divide the remaining 50 g sugar portion into two equal parts, each weighing 25 g. - Place one of the 25 g sugar portions on one side of the balance scale and the other 25 g sugar portion on the other side. - If the scale balances, then the weight of the sugar is 175 g (100 g from the first weighing + 50 g from the second weighing + 25 g from the third weighing). - If the scale does not balance, move to the next step.

4. Final Calculation: - Remove the 25 g sugar portion from the balance scale. - The remaining sugar on the scale weighs 25 g. - Add this weight to the total weight calculated in the previous step. - The final weight of the sugar is 200 g.

Explanation

By using this strategy, we can determine the weight of the sugar accurately using only three weighings on a balance scale. The key idea is to divide the sugar into equal parts and use the weights to compare the different portions. By progressively dividing the sugar and comparing the weights, we can narrow down the weight of the sugar to the desired value.

Example

Let's go through an example to illustrate the solution:

1. First Weighing: - Place one 50 g weight on one side of the balance scale and 100 g of sugar on the other side. - The scale balances, indicating that the weight of the sugar is 100 g.

2. Second Weighing: - Remove the 50 g weight from the balance scale. - Divide the remaining 100 g of sugar into two equal parts, each weighing 50 g. - Place one of the 50 g sugar portions on one side of the balance scale and the other 50 g sugar portion on the other side. - The scale balances, indicating that the weight of the sugar is 150 g (100 g from the first weighing + 50 g from the second weighing).

3. Third Weighing: - Remove the 50 g sugar portion from the balance scale. - Divide the remaining 50 g sugar portion into two equal parts, each weighing 25 g. - Place one of the 25 g sugar portions on one side of the balance scale and the other 25 g sugar portion on the other side. - The scale does not balance.

4. Final Calculation: - Remove the 25 g sugar portion from the balance scale. - The remaining sugar on the scale weighs 25 g. - Add this weight to the total weight calculated in the previous step. - The final weight of the sugar is 175 g.

Conclusion

Using this strategy, we can accurately determine the weight of 2 kg of sugar using the given 9 kg of sugar and two weights of 50 g and 200 g by performing three weighings on a balance scale. The final weight of the sugar is 200 g.

Please let me know if anything is unclear or if you need further assistance!