Question

A   chemist   wants   to   make   24   liters   of   a   20.5%   acid  
solution.   In   the   stock   room   she   finds   a   12%   acid   solution  
and   a   32%   acid   solution.   How   many   liters   of   each   solution  
must   be   mixed   to   obtain   the   desired   solution?   Round   all  
computations   to   the   nearest   thousandth.  

Answer 1

Let the chemist needs x litres of 12% acid solution and y litres of 32% acid solution.

Then according to the given data, we have,

x + y = 24................(1)

and, (12x/100) + (32y/100) = (24 * 20.5/100)

i.e. 12x + 32y = 492............(2)

.

Now 32*(1) - (2) gives,

32x + 32y - 12x - 32y = 768 - 492

i.e. 20x = 276

i.e. x = 276/20

i.e. x = 13.8

So from (1), y = 24 - 13.8 = 10.2

.

.

So the chemist needs 13.8 litres of 12% acid solution and 10.2 litres of 32% acid solution.