$7200.. you would find out what 3.5% of $6000 (210) is and then multiply it by 6 (1200) and then add it to the original $6000
He would place 60 balloons in each room. First you subtract 13 from 313 and get 300. Then you divide 300 by 5 which brings you to the answer of 60 balloons per room.
We're looking for
such that
, which requires



Integrating both sides of the first PDE wrt
gives

Differenting this wrt
gives


but we're assuming
is a function that doesn't depend on
, which is contradicted by this result, and so there is no such
and
is not conservative.