Answer:
Step-by-step explanation:
Let's begin by assigning letters to represent our two unknowns:
x (liters of 25% solution)
y (liters of 50% solution)
Our system of equations will consist of two equations:
Equation #1 (total volume of solution)
Equation #2 (total concentration of acid)
Our total volume of solution is 10 liters, which can be expressed as the sum of our unknowns:
Equation #1: x + y = 10
Our total concentration of acid can be expressed as the sum of the individual acid concentrations to make up the concentration of the final solution:
Equation #2: (0.25)(x) + (0.50)(y) =
(0.40)(10)
We can use Equation #1 to express one unknown in terms of the other and then plug that expression into Equation #2 to solve for one of the unknowns:
x + y = 10
y = 10 - x
Now we'll plug our expression for y in terms of x into Equation #2 and solve for x:
0.25(x) + 0.50(10 - x) = 0.40(10)
0.25x + 5 - 0.50x = 4
-0.25x = 4 - 5
-0.25x = -1
x = (-1)/(-0.25)
x = 4 (liters of 25% solution)
Now we'll plug our value for x into Equation #1 and solve for y:
4 + y = 10
y = 10 - 4
y = 6 (liters of 50% solution)
Finally, we will verify the correctness of our answers by plugging these values into Equation #2 to see if the sum of the component acid concentrations equals the final solution concentration:
0.25(4) + (0.50)(6) = 0.40(10)
1 + 3 = 4
4 = 4 (our answers are correct)
