Let x be the liters need of the 25% acid solution, and y be the 70% acid solution, then we can set the following system of equations:
[tex]\begin{gathered} x+y=90, \\ 0.25x+0.70y=0.40(90)=36. \end{gathered}[/tex]
Solving the first equation for x, we get:
[tex]x=90-y\text{.}[/tex]
Substituting the above equation in the second equation we get:
[tex]0.25(90-y)+0.70y=36.[/tex]
Simplifying and adding like terms we get:
[tex]\begin{gathered} 22.5-0.25y+0.70y=36, \\ 0.45y+22.5=36. \end{gathered}[/tex]
Adding 22.5 and then dividing by 0.45 we get:
[tex]\begin{gathered} 0.45y=13.5, \\ y=30. \end{gathered}[/tex]
Substituting y=30 in x=90-y, we get:
[tex]x=90-30=60.[/tex]
Therefore, x=60 liters, and y=30 liters.
Answer: 60 liters of the 25% acid solution are needed and 30 liters are needed of the 70% acid solution.
