How many liters of a 60% acid solution must be mixed with a 30% acid solution to get 270 L of a 50% acid solution? ____ liters of a 60% acid solution must be used.
Let there be V1 litres of 60% solution and V2 litres of 30% solution
Hence, V1 + V2 = 270
V1 litres of 60% solution = 0.6*V1 litres acid
V2 litres of 30% solution = 0.3*V2 litres acid
270 litres of 50% solution = 0.5*270 litres acid
Hence,
0.6*V1 + 0.3*V2 = 0.5*270
V1 + V2 = 270
Substituting for V1 = 270 – V2 into the 1st equation,
0.6*(270 – V2) + 0.3*V2 = 0.5*270
162 – 0.6*V2 + 0.3*V2 = 135
162 – 0.3*V2 = 135
0.3*V2 = 27
V2 = 90
V1 = 270 – 90 = 180
Answer: Mix together 180 litres of 60% solution with 90 litres of 30% solution