How many liters of peroxide should be added to 12 liters of an 8% peroxide solution so that the remaining solution contains 16% peroxide?
solve for x, the amount to be added
x + .08(12) = .16(x+12)
jbh
To solve this problem, we need to use the concept of mixtures.
Step 1: Let's determine the amount of pure peroxide in the original 12 liters of 8% peroxide solution.
The original solution contains 8% peroxide, which means 8% of the 12 liters is pure peroxide.
Amount of pure peroxide = (8/100) * 12 liters = 0.96 liters
Step 2: Let's assume we need to add x liters of pure peroxide to achieve a 16% peroxide solution.
Step 3: Now, we know that the total volume of the final solution will be 12 + x liters.
Step 4: The amount of pure peroxide in the final solution will be the sum of the pure peroxide from the initial solution and the pure peroxide added.
The total amount of pure peroxide = 0.96 liters + x liters
Step 5: The concentration of peroxide in the final solution should be 16%, which means the amount of pure peroxide should be 16% of the total volume of the final solution.
Amount of pure peroxide = (16/100) * (12 + x) liters
Step 6: Now, equate the amount of pure peroxide from the initial solution and the amount of pure peroxide in the final solution.
0.96 liters + x liters = (16/100) * (12 + x) liters
Step 7: Solve the equation for x.
0.96 + x = (16/100) * (12 + x)
Multiply both sides by 100 to eliminate the denominator:
96 + 100x = 16(12 + x)
96 + 100x = 192 + 16x
84x = 96
x = 96/84
x ≈ 1.14 liters
Therefore, approximately 1.14 liters of peroxide should be added to the 12 liters of an 8% peroxide solution to obtain a final solution with 16% peroxide.