Gabe Amodeo, a nuclear physicist, needs 80 liters of a 30% acid solution. He currently has a 20% solution and a 60% solution. How many liters of each does he need to make the needed 80 liters of 30% acid solution?
Let x be the number of liters of the 20% solution Gabe Amodeo needs and y be the number of liters of the 60% solution he needs.
We know that x + y = 80, so y = 80 - x.
We also know that 0.2x + 0.6y = 0.3(80).
Substituting the value of y from the first equation into the second equation, we get 0.2x + 0.6(80 - x) = 0.3(80).
Simplifying the equation, we get 0.2x + 48 - 0.6x = 24.
Combining like terms, we get -0.4x + 48 = 24.
Subtracting 48 from both sides, we get -0.4x = -24.
Dividing both sides by -0.4, we get x = 60.
Substituting this value back into the equation y = 80 - x, we get y = 80 - 60 = 20.
Therefore, Gabe Amodeo needs 60 liters of the 20% solution and 20 liters of the 60% solution. Answer: \boxed{60 \text{ liters}, 20 \text{ liters}}.