Gabe Amodeo, a nuclear physicist, needs 60 liters of a 60% acid solution. He currently has a 40% solution and a 70% solution. How many liters of each does he need to make the needed 60 liters of 60% acid solution?
Gabe needs liters of the 40% solution.
Let's call the number of liters of the 40% solution that Gabe needs as x.
Therefore, he needs 60 - x liters of the 70% solution.
Now let's calculate the amount of acid in these two solutions:
Amount of acid in the 40% solution = 40/100 * x = 0.4x
Amount of acid in the 70% solution = 70/100 * (60 - x) = 0.7(60 - x) = 42 - 0.7x
To make a 60% acid solution, the amount of acid in the mixture will be:
Amount of acid in the mixed solution = 60/100 * 60 = 0.6 * 60 = 36
Since the amount of acid in the mixed solution equals the sum of the amounts of acid in the 40% and 70% solutions, we can write the equation:
0.4x + 42 - 0.7x = 36
Let's solve this equation to find the value of x:
-0.3x = 36 - 42
-0.3x = -6
x = -6 / -0.3
x = 20
Therefore, Gabe needs 20 liters of the 40% solution.