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I have a list of chemical formulas that are each comprised of a number of base components. Two of the base components contain an additive, $X$. This additive needs to exist in each formula at a concentration of $3\%$. Of the two components, component $A$ contains $X$ at a concentration of $3\%$, $B$ contains $X$ at a concentration of $50\%$. Component $A$ may already exist in some of the formulas in differing quantities. I need to balance the quantities of component $A$ and component $B$ in each formula so the the $X$ additive will be $3\%$.

Unfortunately I can't seem to come up with a formula to describe this relationship. My feeble math skills say that something like $3x + 50x = 3y$ might be a start. Can anyone point me in the right direction?

Ivo Terek
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scumdogg
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  • Thanks for the reply Scott. I should clarify my question. The formulas will contain component A, which I have to replace with component A and B to total 3% of the X component. For example, a formula contains 49.9g of component A, having a total of 1.497 % of X. I need to add an additional 1.502% of X so will do this by adding component B. But the total of both A and B can't exceed 49.9g so by adding B I'd have to reduce A, which would also reduce the X percentage. I hope that makes sense. – scumdogg Jul 16 '14 at 20:36

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If I read your question correctly, I think $$3\%(A) + 50\%(B) = 3\%(A + B + \text{any other components})$$ where $A, B$, etc. are the amounts (volume, mass, whatever) of each component in a formula.

My process:

$3\%$ of your formula needs to be $X$. Since your formula is just the sum of all of its components, I can write it as $A + B + \text{any other components}$. Therefore, the amount of $X$ in your formula is $3\%$ of $A + B + \text{any other components}$.

The amount of $X$ in your formula is accounted for by the amounts of $A$ and $B$ in the formula. Since $3\%$ of $A$ is $X$ and $50\%$ of $B$ is $X$, we can write the amount of $X$ contributed to your formula as $3\%(A) + 50\%(B)$.

Scott Caldwell
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