Calculation when Mixing Two Compounds....

[haubenkoch]

Dear Comunity,

I am running into a (probably pretty simple) problem here, yet the most simple things are sometimes upon me...:(

I have a liquid solution which consists of 70% compound A and 30% compound B.
I also have a bottle with 100% compound A.

What I would like to do is to achieve a concentration of 80% compound A and 20% compound B. Can someone tell me how this is calculated?

I was thinking of something like c1*v1=c2*v2 but this doesn't get me anywhere...am I missing something?

Any help on this would be very much appreciated!

 

[MarkFL]

I would set it up as follows:

Let $x$ be the amount of solution you currently have, the 7:3 mix. Then let $y$ be the amount of 100% compound A you wish to add. Thus we want:

\(\displaystyle 0.7x+y=0.8(x+y)\)

Do you see how both sides of the equation represent the amount of compound A present in the final solution? The left side represents the initial amount of compound A plus the amount added. The right side reflects the fact that we want 80% of the final amount to be compound A.

Now you may solve this for $y$ as a function of $x$. What do you find?

 

[soroban]

Hello, haubenkoch!

We can disregard references to compound B.

I have a liquid solution which is 70% alcohol.
I also have a bottle with 100% alcohol.

I would like a concentration of 80% alcohol.

This is an explanation of MarkFL's solution.Let $$x$$ = liters of 70% alcohol.
It contains $$0.7x$$ liters of alcohol.

We add $$y$$ liters of 100% alcohol.
It contains $$y$$ liters of alcohol.

The mixture contains $$0.7x + y$$ liters of alcohol. .[1]But we know that the mixture will be
. . $$x+y$$ liters which is 80% alcohol.
It contains $$0.8(x+y)$$ liters of alcohol. .[2]We just described the final amount of alcohol in two ways.

There is our equation! ..$$0.7x + y \:=\:0.8(x+y)$$