Elastic and inelastic collisions

[MBBphys]

Homework Statement

In a closed system, in an inelastic collision, momentum and total energy is conserved, but total kinetic energy is not.
But how is this possible? If we have a change in total kinetic energy, we have a change in velocity, and so we must have a change in momentum as:
momentum=mass*velocity
So I am really confused!
Thanks :)

Homework Equations

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The Attempt at a Solution

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[TSny]

Keep in mind that kinetic energy is a scalar quantity and momentum is a vector quantity.

Think about the example of two equal masses moving toward each other with equal speeds and the two masses stick together and come to rest after they collide.