Answer
$$x=12.5$$ $$y=37.5$$
Work Step by Step
Let $x$ be the amount (in cc) of the 6% acid solution and $y$ be the amount (in cc) of the 14% acid solution.
Equation 1: $0.06x+0.14y=0.12(50)$
Equation 2: $x+y=50$
We can solve for the value of $x$ and $y$ using the substitution method.
Using equation 2, subtract $y$ from both sides:
$$x+y-y=50-y$$ $$x=50-y$$
Substitute this equation to equation 1:
$$0.06(50-y)+0.14y=0.12(50)$$ $$3-0.06y+0.14y=6$$ $$3+0.08y=6$$
Subtract $3$ from both sides:
$$3-3+0.08y=6-3$$ $$0.08y=3$$
Divide both sides by $0.08$
$$\frac{0.08y}{0.08}=\frac{3}{0.08}$$ $$y=37.5$$
Substitute this value of $y$ to equation 2:
$$x+37.5=50$$
Subtract $37.5$ from both sides:
$$x+37.5-37.5=50-37.5$$ $$x=12.5$$
Use equation 1 to check:
$$0.06(12.5) + 0.14(37.5) = 0.12(50)$$ $$0.75+5.25=6$$ $$6=6$$
