I have read multiple threads including:

https://physics.stackexchange.com/q/93971/

https://physics.stackexchange.com/q/91003/

https://physics.stackexchange.com/q/599278/

https://physics.stackexchange.com/q/598480/

https://physics.stackexchange.com/q/602734/

https://physics.stackexchange.com/q/511971/

In an elastic collision, I understand that momentum is conserved and kinetic energy is conserved. If billiard ball of silver (with velocity $v(Ag)$ impacts a stationary billiard ball of aluminum, I am trying to calculate the velocity of the aluminum ball after the collision, $v(Al)$. After an elastic collision, the impactor is at rest and the impactee has the motion.

Using momentum, $= m \cdot v$

$$m(Ag) \cdot v(Ag) = m(Al) \cdot v(Al)$$ 

Assuming silver is 4x denser than aluminum, then using momentum, the aluminum ball should have velocity 

$$v(Al) = 4\cdot v(Ag)$$ 

But if we use kinetic energy, $1/2 m \cdot v^2$

$$\frac12m(Ag)\cdot v(ag)^2=\frac12m(Al)\cdot v(Al)^2$$

$$v(Al)^2=\frac{m(Ag)}{m(Al)}\cdot v(Ag)^2$$

$$v(Al)=\left(\frac{m(Ag)}{m(Al)}\right)^{\frac12}\cdot v(Ag)$$

$$v(Al)=2\cdot v(Ag)$$

Somewhere I have lost some neuron connections in my brain because I cannot resolve this conflict. This is a perfectly elastic collision so both momentum and kinetic energy should be conserved.