jmc

The total cost of the peanut butter and jam is $N(4B+5J)=253$ cents, so $N$ and $4B+5J$ are factors of $253=11\cdot 23$. Because $N>1$, the possible values of $N$ are 11, 23, and 253. If $N=253$, then $4B+5J=1$, which is impossible since $B$ and $J$ are positive integers. If $N=23$, then $4B+5J=11$, which also has no solutions in positive integers. Hence $N=11$ and $4B+5J=23$, which has the unique positive integer solution $B=2$ and $J=3$. So the cost of the jam is 11(3)(5\text{ cents})=\boxed{\1.65}$.