You need 270ml of a 5% alcohol solution. On hand, you have a 90% alcohol mixture. How much of the 90% alcohol mixture and pure water will you need to obtain the desired solution?

Question

270 ml

5% alcohol solution

90% alcohol mixture

Answer 1

Let a=amount in mL of the 90% alcohol mixture (10% water), w=amount of 100% pure water (0% alcohol).

a+w=270mL

Consider the amount of alcohol:

0.9a=0.05×270=13.5mL, a=13.5/0.9=15mL.

w=270-15=255mL.

So we need 255mL of pure water and 15mL of 90% alcohol mixture.

(Another way is to consider the amount of pure water:

0.1a+w=0.95×270=256.5,

0.1a+270-a=256.5mL,

13.5=0.9a, a=15mL, w=255mL.)