Originally posted here: How much to increase $A$ so that $B$ becomes $90\%$ of what is was?
If I had a mixture of A and B, and I wanted to increase A so that B drops to 90% of what it was in the solution -- how would I solve this?
For example, say A was 90 grams (90%) and B was 10 grams (10%) for a total of 100 grams. By how much I increase the weight of A so that B becomes 9% (which is 90% of 10%)?
10 grams is 9% of 111.11. Subtract 10 grams from 111.11 grams and you get 101.11 grams. If A was originally 90 grams, then A would need to increase by 11.11.
Expressed in words: Some percentage of A (e.g. Ax) plus some percentage of B (e.g. Bx) equals 100. What value C can we add to Ax so that Bx becomes 90% of it's original contribution to the mixture (e.g. B(x * .9))?
How do I express the above problem as an equation and solve?
The original fraction of $B$ in the solution is $$\frac B{A+B}$$ Now you want to add some amount $a$ to the mixture to reduce this fraction by $10$ perecent: $$\frac{B}{A+a+B}=.9\frac B{A+B}$$ Solve for $a$.