Theresa Morgan, a chemist, has a 15% hydrochloric acid solution and a 65% hydrochloric acid solution. How many liters of each should she mix to get 390.625 liters of a hydrochloric acid solution with a 49% acid concentration?

125 L of 15% and 265.625 L of 65% HCl

Explanation:

let x = volume of 15% HCl, y = 65% HCl

15x + 65y = 49 * 390.625

15x + 65y = 19140.625

x + y = 390.625

x = 390.625 - y

substitute for x in equation 1

15 (390.625 - y) + 65y = 19140.625

5859.375 - 15 y + 65 y = 19140.625

50 y = 19140.625 - 5859.375 = 13281.25

y = 132181.25 / 50 = 265.625 L

X = 390.625 - y = 390.625 - 265.625 = 125 L