Question 706648
Your question is well organized.


a = mls. of solution A
b = mls. of solution B


System to solve:
{{{a+b=800}}}
{{{(30*a+70*b)/800=54}}}


Working first through the rational equation,
{{{((30*a+70*b)/800)*800=54*800}}}
{{{30*a+70*b=54*800}}},
Next, divide both sides by 10 to get in this case integer coefficients.
The rational equation becomes
{{{3a+7b=80*54.}}}

Next we can work with the volume equation and the transformed equation that we just found:
Try subtracting 3 times the volume equation from this new form of what was the rational percentage equation, and you will easily find b.  Find then a as {{{a=800-b}}}.


(What I said is to do this:
3a+7b-(3a+3b)=80*54-3*800,
From that find 7b-3b=1920,
and you see what to do.)