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, $= m \cdot v$

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

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.