I have read multiple threads including:

When is energy conserved in a collision and not momentum?

How to calculate velocities after collision?

How can I calculate the final velocities of two spheres after an elastic collision?

Calculating new velocities of $n$-dimensional particles after collision

Velocities in an elastic collision

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.