college algebra

Question

A seven-gallon jug is full of 30% isopropyl alcohol solution; you wish to drain off some amount of this liquid and replace it wih 90% isopropyl in order to get a solution which is 75% isopropyl (and thus usable as hand sanitizer). How many gallons should you drain and replace?

Answer 1

30(7) - 30X + 90X = 75(7)

60X = 45(7)

4X = 3(7)=21

X = 21/4 = 5.25 liters replacing 30 with 90 to get 7 liters of 75%