Question

Смешав 15% и 25% растворы соли, получили 5 кг 20 % раствора соли Сколько килограммов каждого раствора смешали? Решите задачу с помощью системы уравнений

Answer 1

X+y=5      x=5-y
-        
0.15x+0.25y=1
0.85x+0.75y=4
0.85(5-y)+0.75=4
4.25-0.85y+0.75y=4
-0.1y=-0.25
y=2.5 кг. 25%
x´=5-2.5=2.5 кг. 15%

Answer 2

Problem Analysis

We are given two solutions, one with a concentration of 15% and the other with a concentration of 25%. When these two solutions are mixed, a 20% solution with a total weight of 5 kg is obtained. We need to find out how many kilograms of each solution were mixed.

Let's assume that x kg of the 15% solution and y kg of the 25% solution were mixed.

System of Equations

To solve this problem, we can set up a system of equations based on the given information.

Equation 1: The total weight of the mixed solution is 5 kg. x + y = 5

Equation 2: The concentration of the mixed solution is 20%. (0.15x + 0.25y) / (x + y) = 0.20

Now, let's solve this system of equations to find the values of x and y.

Solving the System of Equations

We can solve the system of equations using substitution or elimination. Let's use substitution.

From Equation 1, we have: x = 5 - y

Substituting this value of x into Equation 2, we get: (0.15(5 - y) + 0.25y) / (5 - y + y) = 0.20

Simplifying the equation: (0.75 - 0.15y + 0.25y) / 5 = 0.20 (0.75 + 0.10y) / 5 = 0.20 0.75 + 0.10y = 0.20 * 5 0.75 + 0.10y = 1.00 0.10y = 1.00 - 0.75 0.10y = 0.25 y = 0.25 / 0.10 y = 2.5

Now, substituting the value of y back into Equation 1, we get: x + 2.5 = 5 x = 5 - 2.5 x = 2.5

Therefore, we mixed 2.5 kg of the 15% solution and 2.5 kg of the 25% solution.

Answer

We mixed 2.5 kg of the 15% solution and 2.5 kg of the 25% solution.