Question 271748
(liters of alcohol in final solution)/(liters of final solution) = 50%
Let {{{a}}} = liters of 30% solution to use
Let {{{b}}} = liters of 80% solution to use
given:
{{{a + b = 100}}}
{{{.3a}}} = liters of alcohol in 30% solution
{{{.8b}}} = liters of alcohol in 80% solution
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(1) {{{(.3a + .8b) / 100 = .5}}}
(2) {{{a + b = 100}}}
from (1)
(1) {{{.3a + .8b = 50}}}
(1) {{{3a + 8b = 500}}}
Multiply both sides of (2) by {{{3}}}
and subtract from (1)
(1) {{{3a + 8b = 500}}}
(2) {{{-3a - 3b = -300}}}
{{{5b = 200}}}
{{{b = 40}}}
and, from (2)
{{{a + 40 = 100}}}
{{{a = 60}}}
60 liters of the 30% solution and 40 liters 
of the 80% solution are needed
check:
(1) {{{(.3a + .8b) / 100 = .5}}}
{{{(.3*60 + .8*40) / 100 = .5}}}
{{{(18 + 32)/100 = .5}}}
{{{50/100 = .5}}}
{{{.5 = .5}}}
OK