A 12% solution and a 24% solution are to be mixed to create 80 mL of a 16% solution. How much of each should be used?
Is the correct answer 53 1/3 L of the 12% solution and 26 2.3 of the 24% solution?
To solve this problem, we can use a method called "mixture problem" or "mixture equation." Let's break down the steps on how to solve this:
Step 1: Understand the information given:
- We need to mix a 12% solution and a 24% solution together.
- The total volume of the mixture should be 80 mL.
- The resulting mixture should have a concentration of 16%.
Step 2: Set up the equation:
Let's assume that x mL of the 12% solution is used, while the remaining (80 - x) mL will be the 24% solution.
From here, we can calculate the amount of pure substance in each solution:
- Amount of pure substance (12% solution) = 12/100 * x mL
- Amount of pure substance (24% solution) = 24/100 * (80 - x) mL
Now, we need to set up the equation:
12/100 * x mL + 24/100 * (80 - x) mL = 16/100 * 80 mL
Step 3: Solve the equation:
Let's simplify the equation and solve for x:
0.12x + 0.24(80 - x) = 0.16 * 80
0.12x + 19.2 - 0.24x = 12.8
-0.12x + 19.2 = 12.8
-0.12x = 12.8 - 19.2
-0.12x = -6.4
x = -6.4 / -0.12
x ≈ 53.33 mL
Step 4: Calculate the amount of the other solution:
We previously assumed that x mL of the 12% solution was used. So, the amount of the 24% solution would be (80 - x) mL.
Substituting x = 53.33 mL:
(80 - 53.33) mL = 26.67 mL
Therefore, the correct answer is approximately 53.33 mL of the 12% solution and 26.67 mL of the 24% solution.
So, the answer you provided, 53 1/3 L of the 12% solution and 26 2.3 of the 24% solution, is not correct.
No, the correct answer is not 53 1/3 L of the 12% solution and 26 2.3 of the 24% solution. The correct answer for the amount of each solution to be used is as follows:
Let's assume the amount of the 12% solution used is 'x' mL.
Since the total volume of the final solution is given as 80 mL, the amount of the 24% solution used would be 80 - x mL.
Now, let's set up the equation based on the percentage of the two solutions:
(12%x + 24%(80-x)) / 80 = 16 / 100
Simplifying the equation:
0.12x + 0.24(80 - x) = 0.16 * 80
Solving for x:
0.12x + 19.2 - 0.24x = 12.8
-0.12x = -6.4
x = -6.4 / -0.12
x = 53.33
Therefore, you would need to use approximately 53.33 mL of the 12% solution and approximately 26.67 mL of the 24% solution.