Solver Mixing Acids

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Source code of 'Mixing Acids'

This Solver (Mixing Acids) was created by by bmauger(101)

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==section input
You have two solutions (A & B) of acid dissolved in water. Acid A has a percentage of acid as *[input acidA=38] percent. Acid B has *[input acidB=88]%. If you want to create *[input totalV=200]ml of an acid at *[input acidT=55]% what volume of each solution do you need?

Volume A: _____ ml
Volume B: _____ ml

Note: Final percentage must be between the two percentages, or it won't be solvable. (i.e. you can't make either a 40 or a 90% acid solution by combining volumes of 50% and 80% solutions).

==section solution

This problem can be solved by a system of equations. The first step though is to define your variables correctly. Because our unknowns are volumes, we can call the volume of solution A a and the volume of B b.
We know from the problem that the total volume is $totalV. Since that total is made up of combining A & B, we can write it as their sum:
{{{a+b=$totalV}}}

The other equation is devised by realizing that the amount of acid contributed by each solution is equal to its volume times its percentage. Thus acid a would contribute a times $acidA and b would contribute b * $acidB.  The final volume of acid will also be equal to the ($totalV) times the final percentage of this solution ($acidT). This gives:
{{{$acidA*a+$acidB*b=$totalV*$acidT}}}

We have now successfully converted from English to math and can solve our two equations. In this example, it's easier done with substitution. Rewriting our first equation solving for a, we get:
{{{a=$totalV-b}}}

Substituting this into to equation 2 for a gives:
{{{$acidA * ($totalV-b) + $acidB*b = $totalV*$acidT}}} Distributing on left & solving right side gives: *[assign aV=$acidA*$totalV] *[assign totalacid=totalV*acidT]
{{{$aV - $acidA(b) + $acidB*b = $totalacid}}} Rearrange combining b's and constants to get: *[assign bs=acidB-acidA] *[assign cons=totalacid-aV]
{{{$bs*b=$cons}}}Dividing both sides by $bs gives: *[assign volB=(cons/bs)]
{{{b=$volB}}} don't forget the units mL.
This can then be put back into the equation:
{{{a=$totalV-b}}}substituting for b gives:
{{{a=$totalV-$volB}}} giving the volume a as: *[assign volA=totalV-volB]
{{{a=$volA}}} mL.

==section output
volB
volA

==section check
acidA=38 acidB=88 totalV=200 acidT=55 volA=132 volB=68