Answer: First: 20% Second: 8%
Step-by-step explanation:
Let's solve the problem step by step to find the concentrations of sulfuric acid in the original containers.
Let's denote the concentration of the first solution as x% and the concentration of the second solution as y%.
For the first blending:
- We mix 200 mL of the first solution with x% concentration with 400 mL of the second solution with y% concentration.
- The resulting mixture has an acid concentration of 11%.
- We can set up the following equation: (200 mL * x% + 400 mL * y%) / (200 mL + 400 mL) = 11%.
For the second blending:
- We mix 300 mL of the first solution with x% concentration with 900 mL of the second solution with y% concentration.
- The resulting mixture has an acid concentration of 9 1/2%, which is equivalent to 9.5%.
- We can set up the following equation: (300 mL * x% + 900 mL * y%) / (300 mL + 900 mL) = 9.5%.
Now, let's solve these equations to find the values of x and y:
Equation 1: (200x + 400y) / 600 = 11
Equation 2: (300x + 900y) / 1200 = 9.5
Simplifying Equation 1:
200x + 400y = 11 * 600
200x + 400y = 6600
Simplifying Equation 2:
300x + 900y = 9.5 * 1200
300x + 900y = 11400
Now, we can solve these two equations simultaneously to find the values of x and y.
Multiplying Equation 1 by 3:
600x + 1200y = 19800
Subtracting Equation 2 from the above equation:
(600x + 1200y) - (300x + 900y) = 19800 - 11400
300x + 300y = 8400
Dividing the above equation by 300:
x + y = 28
Now, we have a system of equations:
200x + 400y = 6600
x + y = 28
Solving these equations simultaneously, we find:
x = 20%
y = 8%
Therefore, the concentration of sulfuric acid in the original containers is:
- The first solution: 20%
- The second solution: 8%