Question 195302
Let x=amount of 30% solution needed

Now we know that the amount of pure alcohol in the 30% mixture (0.30x) plus the amount of pure alcohol in the 40 liters (0.90*40) has to equal the amount of pure alcohol in the final mixture (0.50(40+x), so:

0.30x+0.90*40=0.50(40+x)  get rid of parens
0.30x+36=20+0.50x  subtract 36 and also 0.50x from each side
0.30x-0.50x+36-36=20-36
-0.20x=-16  divide each side by -0.20
x=80 liters-------------------amount of 30% solution needed

CK
0.30*80+0.90*40=0.50(120)
24+36=60
60=60

Hope this helps---ptaylor