Answer
$\text{10 liters of 30% solution, and 4 liters of 65% solution.}$
Work Step by Step
Let us consider that $\text{x=liters of 30% solution, and}$ $\text{y =liters of 65% solution}$
We are given:
$x+y=14~~~~(1) $
and
$0.30x+0.65y=0.40(14)~~~~(2)$
Re-write equation (1) as: $y=14-x~~~~(3)$
Here, the first equation indicates the amounts of solutions in litres and the second indicates litres of pure acid in the mixture.
We substitute equation (3) into equation (2):
$0.30x+0.65(14−x)=0.40(14) \\
30x+65(14−x)=40(14)\\
−35x=−350\\
x=10 \ liters$
Now, back substitute the value of $x$ into Equation (3) to solve for $y$: $y=14-10=4 \ liters$
Therefore, our desired results are:
$\text{10 liters of 30% solution,, and 4 liters of 65% solution.}$
