Two blocks of mass $M_1$ and $M_2$ moving along a 1-dimensional straight line with velocities $V_1$ and $V_2$, respectively, collide elastically. After the collision they move with respective velocities $U_1$ and $U_2$. What is the ratio $M_1/M_2$ if the velocities are to be interchanged, ie, $U_1=V_2$ and $U_2=V_1$?
I'm very confused as to where to begin in regards to this question. I've tried rearranging the conversation of momentum equation ($m_1v_1 + m_2v_2 = m_1u_1 + m_2u_2$) to express it in terms of $m_1$ and $m_2$ and then dividing them into each other. However this leaves me with $m_1$ and $m_2$ on both sides which is definitely incorrect. Is there an easier way to find the ratio?