It probably is implicitely assumed a price is an integer number of cents. There are $20\cdot 20 = 400$ prices $c_i+s_j$ for a cat in a sack, and these prices are bounded by $12.10$ to $16$ dollars. But there are only $391$ possible prices in that range, so we must have some $c_i+s_j = c_k+s_\ell$. Clearly $i=k$ if and only if $j=\ell$, so we're done.