Question

Смешав 14-процентный и 50-процентный растворы кислоты и добавив 10 кг чистой воды,получили 22-процентный раствор кислоты. Если бы вместо 10 кг воды добавили 10 кг 50-процентного раствора той же кислоты,то получили бы 32-процентный раствор кислоты.Сколько килограммов 14-процентного раствора использовали для получения смеси?Помогите пожалуйста решить.

Answer 1

0.14x+0.5y=0.22(x+y+10)

0.14x+0.5y+5=0.32(x+y+10)

Решаем систему уравнений, получаем y=15, x=25. x - количество 14%-ного раствора, y - количество 50%-ного раствора.

Answer 2

Problem Analysis

We are given that by mixing a 14% acid solution and a 50% acid solution and adding 10 kg of water, we obtain a 22% acid solution. If instead of adding 10 kg of water, we added 10 kg of a 50% acid solution, we would obtain a 32% acid solution. We need to determine how many kilograms of the 14% acid solution were used to obtain the mixture.

Solution

Let's assume that x kg of the 14% acid solution were used.

To find the amount of acid in the resulting mixture, we can use the equation:

0.14x + 0.50(10) = 0.22(x + 10)

Simplifying the equation:

0.14x + 5 = 0.22x + 2.2

0.14x - 0.22x = 2.2 - 5

-0.08x = -2.8

x = -2.8 / -0.08

x = 35

Therefore, 35 kg of the 14% acid solution were used to obtain the mixture.

Answer

35 kg of the 14% acid solution were used to obtain the mixture.

[SOURCE 2]