We can express this as a system of equations.
Let x be the liters of the 50%-acid solution and y the liters of the 75%-acid solution.
We then need 2 equations to solve this.
One equation is the total amount of liters (70 liters) that is equal to the sum of the amount of each solution:
[tex]x+y=70[/tex]The second equation is the final concentration, that is a weighted average of the concentration of each solution:
[tex]0.5\cdot x+0.75\cdot y=0.7\cdot70=49[/tex]Then, we can solve this by substitution:
[tex]x+y=70\longrightarrow y=70-x[/tex][tex]\begin{gathered} 0.5x+0.75y=49 \\ 0.5x+0.75(70-x)=49 \\ 0.5+52.5-0.75x=49 \\ -0.25x=49-52.5 \\ -0.25x=-3.5 \\ x=\frac{3.5}{0.25} \\ x=14 \end{gathered}[/tex]Then, we can calculate y as:
[tex]y=70-x=70-14=56[/tex]Answer: we need 14 liters of the 50% acid solution and 56 liters of the 75% acid solution.
