Advanced Math/Mixture

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Question
Hi Janet,

A storage tank contains a brine composed of 2.5% sodium chloride.  One kilogram of sodium chloride is added, resulting in a 3% concentration.  Calculate original brine amount.


Thanks for your assistance and time.

Answer
mass of solution = x
original amount of sodium chloride = 2.5% of x = 0.025x

After adding 1 kg of sodium chloride:
amount of sodium chloride = 0.025x + 1
mass of solution = x + 1
final concentration = (0.025x + 1)/(x + 1) = 0.03

0.025x + 1 = 0.03(x + 1)
0.025x + 1 = 0.03x + 0.03
0.97 = 0.005x
x = 194

original brine amount = 0.025194 = 4.85 kg

Check:
4.85/194 = 2.5%
(4.85+1)/(194+1) = 3%

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Janet Yang

Expertise

I can answer questions in Algebra, Basic Math, Calculus, Differential Equations, Geometry, Number Theory, and Word Problems. I would not feel comfortable answering questions in Probability and Statistics or Topology because I have not studied these in depth.

Experience

I tutor students (fifth through twelfth grades) and am a Top Contributor on Yahoo!Answers with over 24,000 math solutions.

Publications
Co-author of An Outline of Scientific Writing: For Researchers With English as a Foreign Language

Education/Credentials
I have a Bachelor's degree in Applied Mathematics from the University of California at Berkeley.

Past/Present Clients
George White Elementary School. Homework Help program at the Ridgewood Public Library, Ridgewood, NJ. Individual students.

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