Question 226451
Let {{{x}}} = liters of 30% solution to be used
In words:
(liters of alcohol I end up with)/(total liters at end) = 60%
given:
I am adding {{{.3x}}} liters of alcohol to solution
The solution already contains {{{.8*21 = 16.8}}} liters alcohol
I can now write the equation
{{{(.3x + 16.8)/(21 + x) = .6}}}
{{{.3x + 16.8 = .6*(21 + x)}}}
{{{.3x + 16.8 = 12.6 + .6x}}}
{{{.3x = 16.8 - 12.6}}}
{{{.3x = 4.2}}}
{{{x = 14}}}
14 liters of the 30% solution must be added
check:
{{{(.3x + 16.8)/(21 + x) = .6}}}
{{{(.3*14 + 16.8)/(21 + 14) = .6}}}
{{{(4.2 + 16.8)/35 = .6}}}
{{{21/35 = .6}}}
{{{21 = .6*35}}}
{{{21 = 21}}}
OK