Three spheres identical in size, shape and mass are situated over a surface as indicated in the picture. Initially, $2$ and $3$ are at rest. Sphere labeled $1$ makes a collision with $2$ and as a result $2$ makes a collision with $3$. Find the percentage of kinetic energy which $3$ receives with respect from the initial. Assume that in all collisions the coefficient of restitution (COR) is $0.75$.

The alternatives are as follows:

$\begin{array}{ll}

1.&29\%\\

2.&39\%\\

3.&49\%\\

4.&59\%\\

\end{array}$

For this specific situation, what I attempted was to tackle the problem using the conservation of momentum as follows:

$p_i=p_f$

$mv_1=mu_1+mu_2$

$v_1=u_1+u_2$

Since $e=0.75$

$\frac{1}{4}=\frac{u_{1}-u_{2}}{v_{2}-v_{1}}$

But from this part I end up with many equations; how exactly can I find the percentage which is being asked?