SOLUTION: In the lab, Ann has two solutions that contain alcohol and is mixing them with each other. She uses 400 milliliters less of Solution A than Solution B. Solution A is 10% alcohol an
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Question 1202627: In the lab, Ann has two solutions that contain alcohol and is mixing them with each other. She uses 400 milliliters less of Solution A than Solution B. Solution A is 10% alcohol and Solution B is 13% alcohol. How many milliliters of Solution B does she use, if the resulting mixture has 328 milliliters of pure alcohol? Answer by ikleyn(52915) (Show Source):
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In the lab, Ann has two solutions that contain alcohol and is mixing them with each other.
She uses 400 milliliters less of Solution A than Solution B.
Solution A is 10% alcohol and Solution B is 13% alcohol.
How many milliliters of Solution B does she use, if the resulting mixture
has 328 milliliters of pure alcohol?
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Let the volume of the solution B be x milliliters.
Then the volume of the sdolution A is (x-400) milliliters.
Solution A contributes 0.1*(x-400) mL of the pure alcohol to the mixture.
Solution B contributes 0.13*x mL of the pure alcohol to the mixture.
The sum of contributions is 328 mL of the pure alcohol, so we write this equation
0.13x + 0.1*(x-400) = 328.
Simplify and find x
0.13x + 0.1x - 40 = 328
0.23x = 328 + 40
0.23x = 368
x = 368/0.23 = 1600.
ANSWER. 1600 mL of the solution B was used.
