Question

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?

Answer 1

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%

Answer 2

(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