The conservation of linear momentum and the coefficient of restitution are used to derive a formula in which the fraction of energy transferred throughnbodies in one-dimensional collisions depends upon the coefficient of restitution, the relative masses of the bodies, and the number of bodies involved. The percent of energy transferred is graphed as a function of the coefficient of restitution and the number of particles which constitute a mechanical impedance-matching-taper transformer between two end particles whose mass ratio is one-hundred. A demonstration device illustrating the impedance match is discussed.