Alcohol solute problem

Question

You need a 40% alcohol solution. On hand, you have a 450 mL of a 30% alcohol mixture. You also have 90% alcohol mixture. How much of the 90% mixture will you need to add to obtain the desired solution?

Answer 1

Using Alligation:

HAVE.........WANT........PARTS

30%...............................50......

....................40%.....................

90%..............................10.......

You need 50 parts of the 30% solution and 10 parts of the 90% solution.

The 30% solution is 450 mls or 50 parts, so each part is equal to 450/50 = 9 mls

Thus, the 10 parts of the 90% solution will be equal to 90 mls

Summary:

Take the 450 mls of 30% solution and add 90 mls of the 90 % solution

Using Algebra:

(0.30)(450) + (0.90)(x) = (0.40)(450 + x)

135 + 0.9x = 180 + 0.4x

0.5x = 45

x = 90 mls of the 90% solution

Answer 2

(0.30)(450) + (0.90)x = (0.40)(450 + X)