Question 942425
{{{m}}}= number of male employees; {{{1<=m<=13}}} ;
{{{f}}}=number of female employees; {{{1<=f<=13}}} ;
{{{x}}}=number of envelopes each male employee received;
{{{x+3}}}=number of envelopes each female employee received;
{{{f+m=13}}} ;
{{{m*x=80/2=40}}} and {{{f*(x+3)=40}}} . 
Since each female received more envelopes that each male,
we know that there are less females than males, so
{{{f<13/2=6.5}}} and {{{m>13/2=6.5}}} .
We are looking for two integers, {{{f}}} and {{{m}}} , that
are factors of {{{40}}} ,
add up to {{{13}}} ,  and
{{{1<=f<6.5<m<=13}}} .
The factors of 40 are:
1, 2, 4, 5, 8, 10, 20, and 40.
The only solution is
{{{system(f=5,m=8)}}} .