Question

Для приготовления 3 кг варенья из слив требуется 1400 г сахарного сиропа. Сахарный сироп получают из воды и сахара, взятых в одинаковых количествах по массе. Сколько сливового варенья (в кг) получится. если использовать 2.8 кг сахара ( !!! выполнить задачу в виде уравнения !!! )

Answer 1

3000-1400=1600 гр слив нужно для приготовления 3 кг варенья
находим отношение сиропа и фруктов:
1400:1600. сокращаем, получаем отношение:
7:8
х одна часть, значит
7х сиропа нужно для приготовления сливового варенья
8х слив нужно для приготовления варенья.
7х+8х=15х кг количество полученного варенья
2.8×2=5.6 кг сиропа нужно для варенья. Дальше составляем уравнение

5.6+8х=15х
7х=5.6
х=5.6÷7
х=0.8 кг одна часть.

0.8×15=12 кг варенья получим, если используем 2.8 кг сахара

Answer 2

Problem Analysis

To solve this problem, we need to determine how much plum jam can be made using 2.8 kg of sugar. We know that 1400 g of sugar syrup is required to make 3 kg of plum jam. The sugar syrup is made by combining equal amounts of water and sugar by weight. We need to find the weight of plum jam that can be made using 2.8 kg of sugar.

Solution

Let's assume the weight of water and sugar used to make the sugar syrup is x kg each. Since equal amounts of water and sugar are used, we can write the equation:

x + x = 2.8 kg

Simplifying the equation, we get:

2x = 2.8 kg

Dividing both sides of the equation by 2, we get:

x = 1.4 kg

Therefore, 1.4 kg of water and 1.4 kg of sugar are used to make the sugar syrup.

Now, we need to find the weight of plum jam that can be made using 1.4 kg of sugar. We know that 1400 g of sugar syrup is required to make 3 kg of plum jam. So, we can set up the following proportion:

1.4 kg of sugar syrup / 1400 g = x kg of plum jam / 3000 g

Cross-multiplying and solving for x, we get:

x = (1.4 kg * 3000 g) / 1400 g

Simplifying the equation, we get:

x = 3 kg

Therefore, using 2.8 kg of sugar, we can make 3 kg of plum jam.

Answer

If 2.8 kg of sugar is used, 3 kg of plum jam can be made.

Verification

Let's verify the answer using the given information. We know that 1400 g of sugar syrup is required to make 3 kg of plum jam. The sugar syrup is made by combining equal amounts of water and sugar by weight. So, if we use 2.8 kg of sugar, we would need 2.8 kg of water as well. The total weight of the sugar syrup would be 2.8 kg + 2.8 kg = 5.6 kg. Since 1400 g of this sugar syrup is required to make 3 kg of plum jam, the weight of plum jam that can be made using 2.8 kg of sugar is indeed 3 kg. Therefore, the answer is verified.

Conclusion

Using 2.8 kg of sugar, 3 kg of plum jam can be made.