Question

Смешав 43% и 89% р-ры кислоты и добавив 10 кг чистой воды, получили 69% р-р кислоты. Если бы вместо 10 кг воды добавили 10 кг 50% р-ра той же кислоты, то получили бы 73% р-р кислоты. Сколько кг 43% р-ра использовали для получения смеси?

Answer 1

Пусть х кг - первого раствора, у кг - второго, тогда
0,43х + 0,89у = 0,69(х + у + 10)
0,43х + 0,89у + 10 * 0,5 = 0,73(х + у + 10)

43х + 89у = 69х + 69у + 690
43х + 89у + 500 = 73х + 73у + 730

26х - 20у + 690 = 0       Домножим на 4
30х - 16у + 230 = 0       Домножим на 5

104х - 80у + 2760 = 0
150х - 80у + 1150 = 0

Вычтем из второго уравнения первое

46х - 1610 = 0
х = 1610 / 46 = 35
Ответ: 35

Answer 2

Problem Analysis

We are given two scenarios involving the mixing of acid solutions and water. In the first scenario, we mix a 43% acid solution with an 89% acid solution and add 10 kg of pure water. The resulting solution is a 69% acid solution. In the second scenario, we replace the 10 kg of water with a 10 kg solution that is 50% acid. The resulting solution is a 73% acid solution. We need to determine how much of the 43% acid solution was used to obtain the mixture.

Solution

Let's assume that x kg of the 43% acid solution was used to obtain the mixture.

In the first scenario, when we mix the 43% and 89% acid solutions and add 10 kg of water, the resulting solution is a 69% acid solution. We can set up the following equation to represent the acid concentration in the mixture:

0.43x + 0.89(10 - x) = 0.69(10)

Simplifying the equation:

0.43x + 8.9 - 0.89x = 6.9

0.43x - 0.89x = 6.9 - 8.9

-0.46x = -2

x = -2 / -0.46

x ≈ 4.35 kg

Therefore, approximately 4.35 kg of the 43% acid solution was used to obtain the mixture.

Answer

Approximately 4.35 kg of the 43% acid solution was used to obtain the mixture.