Question 264699
In order for 1/6 of the female residents
to marry 1/4 of the males, then 1/6 of the
female residents has to equal 1/4 of the males
because marriage is a one-to-one match.
{{{(1/6)*f = (1/4)*m}}}
Multiply both sides by {{{12}}}
(1) {{{2f = 3m}}}
Also, I am given:
(2) {{{f + m = 8000}}}
I can say this because all the residents 
are either male or female
From (2),
{{{m = 8000 - f}}}
Substitute this in (1)
{{{2f = 3*(8000 - f)}}}
{{{2f = 24000 - 3f}}}
{{{5f = 24000}}}
{{{f = 4800}}}
and, from (2)
{{{4800 + m = 8000}}}
{{{m = 3200}}}
There are 4800 female residents and 3200 male residents
check:
{{{(1/6)*f = (1/4)*m}}}
{{{(1/6)*4800 = (1/4)*3200}}}
Multiply both sides by {{{12/100}}}
{{{2*48 = 3*32}}}
{{{96 = 96}}}
OK