How many liters of a 20% solution should be mixed with a 50% solution to get 12 liters of a 30% solution?

Question

How many 20% solutions should be mixed with 50% solutions to obtain 12 liters of 30% solution

Answer 1

If you want 12 L total, then you can say use v L of the 20% solution.  Then you need the rest of it, or 12-v L, to be the 50% solution.

 

You want to end up with 12L OF a 30% solution.  Say this is salt solution.  You would have 30 parts salt for every 100 parts of solution.  And the amount of salt you need in the 12 L of solution could be calculated by:

 

12 L solution x (30 parts salt / 100 parts of solution) = 3.6 parts salt.

 

You would make 3.6 parts salt by adding the volumes of the 2 given solutions:

v L ( 20 parts salt / 100 parts of solution) + ( (12-v) L x (50 parts salt / 100 parts of solution) = 

 

0.2 v + (12-v) (0.5) =

 

0.2v + 6 - 0.5v and we set that to what we want, 3.6

 

-0.3v + 6 = 3.6

 

2.4 = 0.3 v

 

8 = v

 

We set v = to the amount of the 20% percent.  Therefore the amount of the 50% solution would be 12-v, = 12-8, =4L.