We investigate the consequences of the assumption that the high-transverse-momentum particles seen in hadron-hadron collisions are produced by a single, hard, large-angle elastic scattering of quarks, one from the target and one from the beam. The fast outgoing quarks are assumed to fragment into a cascade jet of hadrons. The distributions of quarks in the incoming hadrons are determined from lepton-hadron inelastic scattering data, together with certain theoretical constraints such as sum rules, etc. The manner in which quarks cascade into hadrons is determined from particle distributions seen in lepton-hadron and lepton-lepton collisions supplemented by theoretical arguments. The quark elastic scattering cross section is parametrized in a purely phenomenological way and the choice $\frac{d\hat{\sigma }}{d\hat{t}}=\frac{2.3\times {10}^6}{(-\hat{s}{\hat{t}}^3)}$ μb Ge${\mathrm{V}}^6$ gives a reasonable fit to all the data for hadron + hadron→meson + anything for $p_{\perp }\gtrsim 2$ GeV/c. Many predictions do not depend sensitively on the exact form for $\frac{d\hat{\sigma }}{d\hat{t}}$ and therefore test our basic assumption. The data examined include single-particle production in $\mathrm{pp}$ collisions at various energies and angles. Particle ratios (${\pi }^{+}$, ${\pi }^{-}$, $K^{+}$, $K^{-}$, and $\eta$) are predicted and discussed. In addition, the ratio of production of ${\pi }^0\text{'}\mathrm{s}$ by beams of ${\pi }^{+}$ and protons on a proton target is explained. With this model we have found no serious inconsistency with data, but several predictions for charge ratios and beam ratios at other angles are presented that have yet to be tested experimentally.