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?
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 $3\%(A) + 50\%(B)$.