Answer
$10$ liters of $ 30\%$ solution,
$4$ liters of $ 65\%$ solution
Work Step by Step
Let
$x=$liters of $ 30\%$ solution
$y=$liters of $ 65\%$ solution
What she wants is $\left\{\begin{array}{llll}
x+y & =14 & \Rightarrow y=14-x & (1)\\
& & & \\
0.30x+0.65y & =0.40(14) & (2) &
\end{array}\right.$
The first equation expresses amounts of solutions in liters.
The second equation expresses liters of pure acid in the mixture.
Substitute y into (2)
$0.30x+0.65(14-x)=0.40(14)\qquad.../\times 100$
$30x+65(14-x)=40(14)$
$30x+910-65x=560$
$-35x=-350$
$x=10$ liters
Back-substitute into (1)
$y=14-10=4$ liters.
