Question 155666
There are 2 unknowns in the problem: VOLUME OF ALCOHOL ---> {{{A(Liters)}}}? VOLUME OF OUTPUT SOLUTION---> {{{S[2](Liters)}}}? 
We'll go to the 1st condition: 10% of Alcohol mixed with 90% of 70L of initial solution {{{S[1]}}} to produce 30% of {{{S[2]}}}. To show:
{{{0.10A+70L(0.90)=0.30S[2]}}}
{{{0.10A+63L=0.30S[2]}}} ----------------------> eqn 1
Now, when we add the Volume of {{{A}}} and {{{S[1]}}}, we get the volume of {{{S[2]}}}. To show:
{{{A+S[1]=S[2]}}} --------------------------------> eqn 2
Continuing, {{{A+70L=S[2]}}} ---------------------> eqn 3
Substitute eqn 3 in eqn 1:
{{{0.10A+70L(0.90)=0.30(A+70L)}}}
{{{0.10A+63L=0.30A+21L}}}
{{{63L-21L=0.30A-0.10A}}}
{{{42L=0.20A}}} -----> {{{cross(42L)210L/cross(0.20)=cross(0.20)A/cross(0.20)}}}
{{{A=210L}}} -------------------> volume of Alcohol
: For Volume of {{{S[2]}}}, go back eqn 2:
{{{210L+70=S[2]}}}
{{{S[2]=280L}}} -------------------> volume of output solution
In doubt? go back eqn 1:
{{{0.10(210)+70(0.90)=0.30(280)}}}
{{{21+63=84}}}
{{{84L=84L}}}
thank you
Jojo