Answer
$37.5$ ounces of the $20$% acid and $12.5$ ounces of the $60$% acid
Work Step by Step
Let $x$ be the solution containing $20$% acid. Since when the solutions are mixed, a total of $50$ ounces of mixture is produced, then $50-x$ is the solution containing $60$% acid. Combining these two solutions to produce a $50$ ounce of a $30$% acid solution results to
\begin{array}{l}\require{cancel}
0.20(x)+0.60(50-x)=0.30(50)
.\end{array}
Using the Distributive Property and the properties of equality, the equation above is equivalent to
\begin{array}{l}\require{cancel}
0.20(x)+0.60(50)+0.60(-x)=0.30(50)
\\
0.20x+30-0.60x=15
\\
0.20x-0.60x=15-30
\\
-0.40x=-15
\\
-10(-0.40x)=(-15)(-10)
\\
4x=150
\\
x=\dfrac{150}{4}
\\
x=37.5
.\end{array}
Hence, $37.5$ ounces of $x,$ or the $20$% acid and $12.5$ ounces of the $60$% acid solution are needed.
