Question

A 4% solution of local anesthesia is needed. However, 40 fl oz of a 5% solution is the only type of anesthesia in stock. How much neutral solution containing no anesthesia should be added to the 40 fl oz container of the 5% solution?

Answer 1

Let x be the amount of neutral solution we need to add.
Since we have 40 fl of 5% local anesthesia solution, we have
`(40)( (5)/(100) )=2` fl of pure anesthesia.
After adding neutral solution, our new volume will be
`40+x`. Remember that the concentration of the anesthesia after adding neutral solution should be 5%=0.05, and since the volume of the pure anesthesia won't change, we can relate all the values with the equation:

`(2)/(40+x) =0.04`

`40+x= (2)/(0.04)`

`40+x=50`

`x=10`

We can conclude that we will need to add 10 fl of neutral solution to our 40 fl of 5% anesthesia solution to get 50 fl of 4% anesthesia solution.