  We match the $\pi\pi\to\pi\pi$ scattering amplitudes of Chiral Perturbation
Theory with those from dispersion relations that respect analyticity and
coupled channel unitarity, as well as accurately describing experiment. Their
dependence on the number of colors ($N_C$) is obtained. By varying $N_C$ the
trajectories of the poles and residues (the couplings to $\pi\pi$) of light
mesons, the $\sigma$, $f_0(980)$, $\rho(770)$ and $f_2(1270)$ are investigated.
Our results show that the method proposed is a reliable way to study the $N_C$
dependence in hadron-hadron scattering with final-state interactions.
