Theresa morgan, a chemist, has a 30% hydrochloric acid solution and a 50% hydrochloric acid solution. how many liters of each should she mix to get 420 liters of a hydrochloric acid solution with a 45% acid concentration? liters of 30% hydrochloric acid solution . liters of 50% hydrochloric acid solution .

Let x represent the number of liters of 50% acid Theresa puts into the mix. The the number of liters of 30% acid will be (420-x). The total amount of acid in the final solution will be ...
  0.50x + 0.30(420-x) = 0.45(420)
  0.20x + 126 = 189 . . . . . . . . . . . . . . . simplify
  0.20x = 63 . . . . . . . . . . . . . . . . . . . . . subtract 126
  x = 63/0.20 = 315 . . . . . . . . . . . . . . . liters of 50% solution
  (420-x) = 420-315 = 105 . . . . . . . . . liters of 30% solution

Theresa should mix ...
  105 liters of 30% solution
  315 liters of 50% solution