Question 8065
Let x = the required number of milliliters of pure alcohol. 

Then we have:
 400(15%) + x(100%) = (400+x)(32%) Change the percents to decimals.

400(0.15) + x(1) = (400+x)(0.32)  Simplify and solve for x.

60 + x = 128 + 0.32x  Subtract 0.32x from both sides.
60 + 0.68x = 128 Subtract 60 from both sides.
0.68x = 68 Divide both sides by 0.68
x = 100 ml of pure alcohol is required.

Check:

400(0.15) + 100 = (400+100)(0.32)
60 + 100 = 500(0.32)
160 = 160 Check ok.