Chemist math problem

Question

Theresa Morgan, a chemist, has a 30% hydrochloric acid solution and a 55% hydrochloric acid solution. How many liters of each should she mix to get 437.5 liters of a hydrochloric acid solution with a 45% acid concentration?

Answer 1

Use a weighted average: Let H₁ = Amount of 30% solution and H₂ = Amount of 55% solution

H₁ + H₂ = 437.5 liters

{ (.3)H₁ + (.55)H₂ }/( H₁ + H₂) = .45

Solving using the 2 equations, we find that H₁ = 175 Liters and H₂ = 262.5 Liters