Question 949394
x females, y males, total 13 employees.
{{{x+y=13}}}


Envelopes Per Type:
{{{40/x}}} for females,  {{{40/y}}} for males
because the 80 envelopes split into 40 and 40.


The description about how the envelopes among the gender types relate:
{{{40/x=3+40/y}}}
simplify to 
{{{40y=3xy+40x}}}


Using total employee count substituting for y from it,
{{{40(13-x)-40x-3x(13-x)=0}}}
...doing the further simplification...
{{{highlight_green(3x^2-119x+520=0)}}}


General solution method for a quadratic equation yields:
{{{highlight(x=5)}}}, {{{highlight(y=8)}}}.


<b>Eight male employees.</b>



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The solution process shown here was abbreviated, done thoroughly off-site.