Question 1103857
Let there be {{{N}}} officers.
So for each officer it would cost,
{{{480/N}}}
Increasing the number by two, the cost would be,
{{{480/(N+2)}}}
So the difference is,
{{{480/N-480/(N+2)=12}}}
{{{40/N-40/(N+2)=1}}}
{{{40(N+2)-40N=N(N+2)}}}
{{{40N+80-40N=N^2+2N}}}
{{{N^2+2N-80=0}}}
{{{(N+10)(N-8)=0}}}
Only positive solutions for N make sense here.
{{{N-8=0}}}
{{{N=8}}}