Let $A\subseteq \mathbb{N}$ be a finite set of size $N$. Is it true that, for any fixed $t$, there are$$\ll \frac{2^N}{N^{3/2}}$$many $S\subseteq A$ such that ${\sum }_{n\in S}n=t$?If we further ask that $|S|=l$ (for any fixed $l$) then is the number of solutions$$\ll \frac{2^N}{N^2},$$with the implied constant independent of $l$ and $t$?