Answer
The lab assistant should add 120cc of the 12% saline solution.
Work Step by Step
Let $x$ be the amount (in cc) of the 12% solution and $y$ be the amount of the 16% solution.
Equation 1: $x+80=y$
Equation 2: $0.12x+0.22(80)=0.16y$
Substitute equation 1 to equation 2:
$$0.12x+0.22(80)=0.16y$$ $$0.12x+0.22(80)=0.16(x+80)$$ $$0.12x+17.6=0.16x+12.8$$
Subtract $17.6$ from both sides:
$$0.12x+17.6-17.6=0.16x+12.8-17.6$$ $$0.12x=0.16x-4.8$$
Subtract $0.16x$ from both sides:
$$0.12x-0.16x=0.16x-0.16x-4.8$$ $$-0.04x=-4.8$$
Divide both sides by $-0.04$:
$$\frac{-0.04x}{-0.04}=\frac{-4.8}{-0.04}$$ $$x=120$$
Substitute this value of $x$ to equation 1:
$$x+80=y$$ $$120+80=y$$ $$y=200$$
Check using equation 2:
$$0.12x+0.22(80)=0.16y$$ $$0.12(120)+0.22(80)=0.16(200)$$ $$14.4+17.6=32$$ $$32=32$$