Answer to Question #100259 in Algebra for Gianna Laureano

Question

the Laboratory technician needs to make it a 56 L batch of a 40% acid solution. how can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 20% to get the desired concentration?

Answer 1

1 = 100%

0.2 = 20%

Let x be a volume of 100% solution, y be a volume of 20% solution.

Then

1*x + 0.2*y = 56*0.4,

x+y=56,

1*x + 0.2*y = 22.4,

x= 56-y.

Substituting x=56-y into the first equation

1*(56-y) + 0.2*y = 22.4,

-y +0.2y = -33.6,

-0.8y = -33.6,

0.8y = 33.6,

y=42,

y= 42 L of 20% acid,

x = 56-42,

x= 14 L of 100% acid.

Answer: 14 L of 100% acid, 42 L of 20% acid.