n the lab, Bob has two solutions that contain alcohol and is mixing them with each other. He uses
400
milliliters less of Solution A than Solution B. Solution A is
20%
alcohol and Solution B is
13%
alcohol. How many milliliters of Solution B does he use, if the resulting mixture has
217
milliliters of pure alcohol?
To solve this problem, let's break it down step by step:
Step 1: Set up variables
Let's assume that Bob uses X milliliters of Solution B. Since he uses 400 milliliters less of Solution A, he would use (X - 400) milliliters of Solution A.
Step 2: Calculate the amount of alcohol in each solution
Let's calculate the amount of alcohol in Solution A and Solution B.
Amount of alcohol in Solution A = 20% of (X - 400)
Amount of alcohol in Solution B = 13% of X
Step 3: Calculate the amount of alcohol in the resulting mixture
The resulting mixture contains 217 milliliters of pure alcohol.
Step 4: Set up an equation
We can set up an equation based on the amount of alcohol in the resulting mixture:
Amount of alcohol in Solution A + Amount of alcohol in Solution B = Amount of alcohol in resulting mixture
Thus, the equation becomes:
0.20 * (X - 400) + 0.13 * X = 217
Step 5: Solve the equation
Now, solve the equation for X:
0.20X - 80 + 0.13X = 217
0.33X - 80 = 217
0.33X = 297
X ≈ 900
Therefore, Bob uses approximately 900 milliliters of Solution B.