Elmo makes $N$ sandwiches for a fundraiser. For each sandwich he uses $B$ globs of peanut butter at $4\cent$ per glob and $J$ blobs of jam at $5\cent$ per blob. The cost of the peanut butter and jam to make all the sandwiches is $$ 2.53$. Assume that $B$, $J$, and $N$ are positive integers with $N>1$. What is the cost of the jam Elmo uses to make the sandwiches?
$\mathrm{(A) \ } $ 1.05\qquad \mathrm{(B) \ } $ 1.25\qquad \mathrm{(C) \ } $ 1.45\qquad \mathrm{(D) \ } $ 1.65\qquad \mathrm{(E) \ } $ 1.85$
The peanut butter and jam for each sandwich costs $4B\cent+5J\cent$, so the peanut butter and jam for $N$ sandwiches costs $N(4B+5J)\cent$. 
Setting this equal to $253\cent$:
$N(4B+5J)=253=11\cdot23$
The only possible positive integer pairs $(N , 4B+5J)$ whose product is $253$ are: $(1,253) ; (11,23) ; (23,11) ; (253,1)$
The first pair violates $N>1$ and the third and fourth pairs have no positive integer solutions for $B$ and $J$. 
So, $N=11$ and $4B+5J=23$.
The only integer solutions for $B$ and $J$ are $B=2$ and $J=3$.
Therefore, the cost of the jam Elmo uses to make the sandwiches is $3\cdot5\cdot11=165\cent$ $=  $1.65 \Rightarrow \boxed{\mathrm{D}}$