I have read multiple threads including:

https://physics.stackexchange.com/questions/93971/when-is-energy-conserved-in-a-collision-and-not-momentum

https://physics.stackexchange.com/questions/91003/how-to-calculate-velocities-after-collision

https://physics.stackexchange.com/questions/599278/how-can-i-calculate-the-final-velocities-of-two-spheres-after-an-elastic-collisi

https://physics.stackexchange.com/questions/598480/calculating-new-velocities-of-n-dimensional-particles-after-collision/598524#598524

https://physics.stackexchange.com/questions/602734/velocities-in-an-elastic-collision

https://physics.stackexchange.com/questions/511971/summation-of-the-velocities-before-and-after-an-elastic-collision

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 * v

m(Ag) * v(Ag) = m(Al) * v(Al). 

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

v(Al) = 4 v(Ag). 

But if we use kinetic energy, 1/2 m * v^2

1/2 m(Ag) * v(ag) ^ 2 = 1/2 m(Al) * v(Al) ^ 2

v(Al) ^ 2 = m(Ag)/m(Al) * v(Ag) ^ 2

v(Al) = ( m(Ag)/m(Al) ) ^ 1/2   *   v(Ag)

v(Al) = 2 * 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.