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?
Gabe needs liters of the 20% solution.
Let x be the number of liters of the 20% solution Gabe needs.
Therefore, he needs 80 - x liters of the 60% solution.
The total amount of acid in the 20% solution is 0.2x liters.
The total amount of acid in the 60% solution is 0.6 * (80 - x) liters.
The total amount of acid in the final 30% solution is 0.3 * 80 = 24 liters.
The equation for the total amount of acid is 0.2x + 0.6 * (80 - x) = 24.
Simplifying the equation gives 0.2x + 48 - 0.6x = 24.
Combining like terms gives -0.4x + 48 = 24.
Subtracting 48 from both sides gives -0.4x = -24.
Dividing both sides by -0.4 gives x = 60.
Therefore, Gabe needs 60 liters of the 20% solution. Answer: \boxed{60}.