imc

The peanut butter and jam for each sandwich costs $4B\text{cent}+5J\text{cent}$, so the peanut butter and jam for $N$ sandwiches costs $N(4B+5J)\text{cent}$. Setting this equal to $253\text{cent}$: $N(4B+5J)=253=11\cdot 23$ 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 $3\cdot 5\cdot 11=165\text{cent}$ $=\text{textdollar}1.65\Rightarrow \boxed{\text{textdollar}1.65}$