Alab technician needs a 40% solution of a certain chemical for an experiment, but the lab that she works in only has a 20% solution and a 50% solution in stock. in what ratio should she mix the 20% solution with the 50% solution in order to obtain the 40% solution that she needs?

To determine the volume of both concentration of the solution to make another concentration of solution, we need to set up two equations since we have two unknowns. 

For the first equation, we do a mass balance:

mass of 50% solution + mass of 20% solution = mass of 40% solution
M1 + M2 = M3

For the second equation, we do a component balance,

M1(50%) + M2(20%) = M3(40%)
.50M1 + .20M2 = .40M3

To determine the ratio, we assume we have to make a 100 g of the 40% solution. So, the equation would change to

M1 + M2 = 100

.50M1 + .20M2 = (100)(.40) = 40

Solving for M1 and M2,

M1 = 66.67 g

M2 = 33.33 g

So, the ratio of the 20% and the 50% would be approximately 33.33/66.67 = 0.5.