mixing solutions

Question

how many liters of 30% alcohol solution must be mixed with 20 liters of a 50% solution to get a 40% solution?

Answer 1

20 liters of each, 30% and 50% to get 40 liters of 40% solution

40 is midway between 30 and 50, so you need equal amounts of each. If you use 20 liters of 50% you also need 20 liters of 30%

but if you don't see that, then solve this with an equation

30% = .3, 40% = .4, 50% =.5

.30x + .50(20) = ..40(40) = 16.

.3x = 16-10 = 6

x = 6/.3 = 20 liters of 30%

.30x + .50(20) = (x+20)(.40)

.3x + 10 = .4x + 8

.1x = 10-8 = 2

x = 2/.1 = 20 liters of 30%