Question 219575
Let {{{x}}} = liters of 5% solution to be added
It doesn't say what the drug is mixed with, so I'll
just call it water.
In words:
(liters of drug in final solution)/(liters of drug + water in final solution) = 8%
given:
In {{{20}}} liters of 10% solution, there is
{{{.1*20 = 2}}} liters of drug
In {{{x}}} liters of the 5% solution there is
{{{.05x}}} liters of drug
-------------------------
{{{(2 + .05x)/(20 + x) = .08}}}
{{{2 + .05x = .08*(20 + x)}}}
{{{2 + .05x = 1.6 + .08x}}}
{{{.03x = .4}}}
{{{x = 13.333}}}
The Pharmacist must add 13.333 liters of the 5% solution
check answer
{{{(2 + .05x)/(20 + x) = .08}}}
{{{(2 + .05*13.333)/(20 + 13.333) = .08}}}
{{{2.666/33.333 = .07998}}}
(error due to rounding -OK)