The number of triples (a,b,c) of positive integers which satisfy the simultaneous equations \begin{align*} ab+bc &= 44,\\ ac+bc &= 23, \end{align*} is<spanclass=′latex−bold′>(A)</span>0<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>2<spanclass=′latex−bold′>(D)</span>3<spanclass=′latex−bold′>(E)</span>4