Expert: Socrates - 3/15/2007

Question
A storage tank contains a brine composed of 2.5% sodium chloride.  A 3% concentration is a result of adding one kilogram of sodium chloride.

Calculate original amount of brine.

Thanks for your assistance.

Answer
Let B = the original amount of brine (salt water)

Since the solution is 2.5% sodium chloride (salt),
the original solution contains (.025)B kilograms of sodium chloride.

After adding one kilogram of sodium chloride , the amount of sodium chloride is now 1 + (.025)B kilograms

The total amount of brine is now 1 + B kilograms

The percentage of sodium chloride is now 3%.

So (.03)(1 + B ) is the amount of sodium chloride in the new solution. But we also know that the total amount of sodium chloride in the new solution is 1 + (.025)B

Set these equal

(.03)(1 + B ) = 1 + (.025)B

.03 + .03B = 1 + .025B

.005B = .07

B = .07/.005 = 70/5 = 14 kilograms

The original amount of brine is 14 kilograms