Question 151779
We respect everybody here but there's no harm in trying this one:
Remember the following:
{{{L[a]}}}= liters of acid = unknown????
{{{L[s]}}}= liters of solution = unknown???
{{{L[a1]}}}= final stage of acid when mixed w/ solution
Now, we all know when we add the volume of {{{acid}}} & {{{solution}}} we get 32 Liters. To show:
{{{L[a]+L[s]=L[a1]}}}
{{{L[a]+L[s]=32L}}} -----------------> eqn 1
Now, "percent of concentration" makes the difference on how many "Liters" of acid we need to put. Putting this into eqn,
{{{0.30L[a]a+0.10L[s]=0.15(32)}}} ------------> working eqn
In summary of the working eqn, 30% of Liters of acid + 10% of Liters of solution equals 15% of 32 Liters of the NEW acid solution.
.
In eqn 1 we get, {{{L[s]=32-L[a]}}} and substitute in our working eqn:
{{{0.30L[a]+0.10(32-L[a])=4.8}}}
{{{0.30L[a]+3.2-0.10L[a]=4.8}}}
{{{0.20L[a]=4.8-3.2}}} 
{{{cross(0.20)L[a]/cross(0.20)=1.4/0.20}}}
{{{L[a]=8L}}} ---------------> amount of Acid Solution that must be added.
FOR THE AMOUNT of SOLUTION, go back eqn 1,
{{{8+L[s]=32}}}, {{{L[s]=32-8}}}
{{{L[s]=24L}}} --------------> amount of SOLUTION that must be added.
Besides, {{{L[a]+L[s]=L[a1]}}}
{{{8+24=32}}}
{{{32=32}}}
Thank you,
Jojo