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 $(40)( \frac{5}{100} )=2$ 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:
$\frac{2}{40+x} =0.04$
$40+x= \frac{2}{0.04}$
$40+x=50$
$x=10$

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.