21. 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 make the needed 80 liters of 30% acid solution?
Gabe needs
liters of the 20% solution.
He also needs
liters of the 60% solution.

Let x be the amount (in liters) of 20% solution that Gabe uses, and y the amount (also in L) of the 60% solution.

He needs 80 L of 30% solution, so that

x + y = 80

0.20x + 0.60y = 0.30 (80) = 24

Solve for y in terms of x :

y = 80 - x

Substitute this into the second equation and solve for x :

0.20x + 0.60 (80 - x) = 24

0.20x + 48 - 0.60x = 24

24 = 0.40x

x = 60

Solve for y :

y = 80 - 60

y = 20