A laboratory technician needs to make a 63-liter batch of a 20% acid solution How can the laboratory technician combine a batch of an acid solution that is pure acid with another that is 10% to get the desired concentration?

Let x be the volume (liters) of pure (at 100%) acid needed

Let y be the volume (liters) of the other acid (at 10%) needed

The final solution will be:

a) x + y = 63 liters, AND their respective concentration in acid: is

100% x & 10% : y that will generate 63 liters at 20%

b) x + 0.1 y = 63x 0.2 = 12.6

Let's solve this system of 2 equations:

x + y = 63

x + 0.1 y = 12.6

Solving it will give you:

x = 7 liters at 100%

y = 56 liters at 10%

(63-x) = amount of 10% solution wanted

0.10 (63-x) + x = 0.20 (63) =

6.3-0.1x+x=12.6

0.9x=6.3

X=7

63-7 = 56 liters

Check:

0.10 (56) + 7 = 0.2 (63)

12.6 = 12.6