In the lab, deandre has two solutions that contain alcohol and is mixing them with each other. He uses 3 times as much solution A as solution B. Solution A is 12% alcohol and solution B is 19% alcohol. How many millimeters of solution B does he use, if the resulting mixture has 330 millimeters of pure alcohol?

a = amount of solution A used

b = amount of solution B used

a + b = 330 (mL, not mm)

Each mL of x% alcohol solution contributes x/100 mL of alcohol; in order to end up with a mixture that is pure alcohol, all 330 mL of the mix needs to be alcohol:

0.12a + 0.19b = 330

Deandre uses 3 times as much of solution A as he does of solution B, so that

3a = b

in which case

a + 3a = 330 = => 4a = 330 = => a = 82.5 = => b = 247.5

But

0.12a + 0.19b = 56.925 ≠ 330