Gabe Amodeo, a nuclear physicist, needs 30 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution. How many liters of each does he ne make the needed 30 liters of 60% acid solution?
Let x be the number of liters of the 40% solution and y be the number of liters of the 70% solution.
We know that x + y = 30 (equation 1) and 0.4x + 0.7y = 0.6 * 30 (equation 2).
Simplifying equation 2, we get 0.4x + 0.7y = 18.
Multiplying equation 1 by 0.4, we get 0.4x + 0.4y = 12.
Subtracting this equation from equation 2, we get 0.7y - 0.4y = 18 - 12.
0.3y = 6.
Hence, y = 6 / 0.3 = 20.
Substituting the value of y in equation 1, we get x + 20 = 30.
x = 30 - 20 = 10.
Gabe needs 10 liters of the 40% solution and 20 liters of the 70% solution to make the needed 30 liters of 60% acid solution. Answer: \boxed{10}.