Alcohol solution problem

Question

You need 260 mL of a 95% alcohol solution. On hand, you have a 35% alcohol mixture. How much of the 35% alcohol mixture and pure alcohol will you need to obtain the desired 95% solution?

Answer 1

Using alligation:

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

35%...................................5.......

......................95%......................

100%................................60......

You need 5 parts of the 35% and 60 parts of the 100% (pure) alcohol

This is a total of 65 parts and the total volume needed is 260 mls

Thus, each part = 260/65 = 4 mls

Summary:

4 mls x 5 = 20 mls of the 35%

4 mls x 60 = 240 mls of the 100% (pure)

Mix 20 mls of the 35% alcohol with 240 mls of the pure alcohol to obtain 260 mls of 95% alcohol

Using algebra:

(x ml)(35%) + (100%)(260 ml - x ml) = (260 ml)(95%)

35x + 26000 - 100x = 24,700

-65x = -1300

x = 20 mls of 35%

260 - 20 = 240 mls of 100%

Answer 2

(0.35)(260 - x) + (1.00)x = (0.95)(260)