Question

Помогите пожалуйста!!! Смешав 41-процентный и 63-процентный растворы кислоты и добавив 10 кг чистой воды ,получили 49-процентный раствор кислоты.Если бы вместо 10 кг воды добавили 10 кг 50-процентного раствора той же кислоты,то получили бы 54-процентный раствор кислоты.Сколько килограммов 41-процентного раствора использовали для получения смеси?

Answer 1

 пусть х масса 41-% раствора

0.49(x+y+10)=0.41x+ 0.63 y

0.54(x+y+10)=0.41+0.63y+5 

\left \{ {{ 0.49(x+y+10)=0.41x+ 0.63 y } \atop { 0.54(x+y+10)=0.41+0.63y+5  }} \right

 \left \{ {0.14y =0.08x+ 4.9} \atop {0.09y=0.13x+0.4}} \right

 \left \{ {{14y=8x+490} \atop {9y=13x+40}} \right

\left \{ {{9*14 y=72x+4410} \atop {9*14y=182x+560y}} \right

110x- 3850=0

 

 x=35

 

 

 

 

 

Answer 2

Calculation of the Amount of 41% Acid Solution Used

To determine the amount of 41% acid solution used to obtain the mixture, we can set up an equation based on the given information.

Let's assume that x kilograms of the 41% acid solution were used.

According to the problem, when 41% acid solution and 63% acid solution are mixed and 10 kg of water is added, a 49% acid solution is obtained.

The equation can be set up as follows:

0.41x + 0.63(10 - x) = 0.49(10)

Simplifying the equation:

0.41x + 6.3 - 0.63x = 4.9

Combining like terms:

-0.22x = -1.4

Dividing both sides by -0.22:

x = 6.36

Therefore, approximately 6.36 kilograms of the 41% acid solution were used to obtain the mixture.