Mixture question

Question

A laboratory technicians needs to make a 21-liter batch of a 40% acid solution. How many the laboratory technicians combine a batch of an acid solution that is pure acid with that is 10% to get the desired concentration?

Answer 1

A 21L batch of 40% acid solution is 40% acid and 60% something else.  We don't care about the something else.  We only care about the acid.  40% of 21L is 8.4L.  Therefore, we want the amount of acid when finished mixing to be 8.4L.

 

Let x = the number of liters of pure solution and y = the number of liters of 10% acid solution.  

 

Since the pure acid is 100% acid, if we include x liters of it, we are adding x liters of acid.

Since the 10% solution is 10% acid, if we include y liters of it, we are adding 10% of y or .1y liters of acid.

 

x + y = 21 (since we don't want more than 21 liters total)

x + .1y = 8.4 (Since only 8.4 liters should be acid).

 

Solving the first equation for y, give us:

y = 21 - x

 

You can use it to replace y in the second equation:

x + .1(21 - x) = 8.4

 

Solving:

x + 2.1 - .1x = 8.4

.9x + 2.1 = 8.4

.9x = 6.3

x = 7

 

Therefore, you should use 7 liters of pure acid and 21-7 or 14 liters of 10% acid solution to get 21 liters of 40% solution.