In the lab, Teresa has two solutions that contain alcohol and is mixing them with each other. Solution A is 2% alcohol and Solution B is 6% alcohol. She uses 600 milliliters of Solution A. How many milliliters of Solution B does she use, if the resulting mixture is a 3% alcohol solution?NumberofmillilitersofSolutionB:
Question
In the lab, Teresa has two solutions that contain alcohol and is mixing them with each other. Solution A is 2% alcohol and Solution B is 6% alcohol. She uses 600 milliliters of Solution A. How many milliliters of Solution B does she use, if the resulting mixture is a 3% alcohol solution?NumberofmillilitersofSolutionB:
Solution
To solve this problem, we can use the concept of weighted averages.
Step 1: Let's denote the amount of Solution B that Teresa uses as x.
Step 2: The amount of alcohol in Solution A is 2% of 600 ml, which is 0.02 * 600 = 12 ml.
Step 3: The amount of alcohol in Solution B is 6% of x, which is 0.06 * x.
Step 4: The total amount of alcohol in the final solution is 3% of the total volume, which is 0.03 * (600 + x).
Step 5: Since the amount of alcohol in the final solution is the sum of the alcohol in Solution A and Solution B, we can set up the following equation:
12 + 0.06x = 0.03 * (600 + x)
Step 6: Simplify the equation to solve for x:
12 + 0.06x = 18 + 0.03x
0.03x = 6
x = 6 / 0.03
x = 200 ml
So, Teresa needs to use 200 milliliters of Solution B.
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