10% Sodium + 30% Sodium

Date: 07/09/2003 at 22:46:04
From: Medrano
Subject: Word problem

A group of chemists are conducting an experiment to produce a new 
liquid material. One chemical contains 15% sodium (Na) and the other 
chemical contains 30% sodium (Na). Once they mix the two samples the 
resulting chemical contains 22% sodium (Na). How many milliliters 
(ml) of each sample must be mixed to obtain 600 ml of the new 
chemical?

Date: 07/11/2003 at 09:17:23
From: Doctor Ian
Subject: Re: Word problem

Hi Alex, 

Instead of jumping in with calculations, let's see if we can just make
sense of the problem in a way that will lead us to a solution. 

Since the first material is 15% sodium, it means that if we have some
amount, A, of the material, we can determine the amount of sodium it
contains by taking 15% of that. Does that make sense?

  amount of sodium from first material = 0.15*A

For example, if we have 100 ml of the material, then 15 ml of it will
be sodium, and 85 ml will be something else. 

Similarly, if B is the amount of the second material,

  amount of sodium from second material = 0.30*B
  
Now, if we combine the two chemicals to get a new chemical, which is
22% sodium, then the total amount of combined sodium is

  amount of sodium from both sources = 0.22*(A+B)

So we can use that to set up an equation:

  sodium from        sodium from        sodium from
  first material  +  second materal  =  both materials

  0.15*A          +  0.30*B          = 0.22*(A+B)

Now, this is kind of a problem, since we have two variables but only
one equation. But in fact, we _have_ a second equation, because we
know that 

  A + B = 600

So now you have two equations, and you can use substitution or
elimination to find the values of the variables:

   Substitution and Elimination
   http://mathforum.org/library/drmath/view/57307.html 

- Doctor Ian, The Math Forum
  http://mathforum.org/dr.math/