Answer
$x=22,y=14$
Work Step by Step
Given: $x+y=36$ and $1180x+125y=27710$
After plugging first equation in second equation, we have
$1180(36-y)+125y=27710 \implies -1055y=-14770$
or, $y=14$
Now, $x+14=36$
or, $x=36-14=22$
Thus, $x=22,y=14$