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/
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