Question 201890
Let {{{a}}} = liters of alcohol in original mixture
Let {{{w}}} = liters of water in original mixture
given:
(alcohol in original mixture)/(water in original mixture) = 4/3
{{{a/w = 4/3}}}
Multiply both sides by {{{3w}}}
{{{3a = 4w}}}
{{{w = (3/4)*a}}} liters
{{{a / ((3/4)*a + 7) = 3/4}}}
Multiply both sides by {{{(3/4)*a + 7}}}
{{{a = (3/4)*((3/4)*a + 7)}}}
{{{a = (9/16)*a + 21/4}}}
{{{16a = 9a + 84}}}
{{{7a = 84}}}
{{{a = 12}}}
There are 12 liters of alcohol in the mixture
check:
{{{a / ((3/4)*a + 7) = 3/4}}}
{{{12 / ((3/4)*12 + 7) = 3/4}}}
{{{12 / (9 + 7) = 3/4}}}
{{{12/16 = 3/4}}}
{{{3/4 = 3/4}}}
OK