We present high-statistics results on the reactions $a+p\ensuremath{\rightarrow}c+X$ where $a$ and $c$ can be any of ${\ensuremath{\pi}}^{\ifmmode\pm\else\textpm\fi{}}$, ${K}^{\ifmmode\pm\else\textpm\fi{}}$, $p$, or $\overline{p}$. The data were taken at 100 and 175 GeV/c incident momenta using the Fermilab Single-Arm Spectrometer operated over the kinematic range $0.2<x<1.0$ and ${p}_{t}<~1.0$ GeV/c. Investigating the $x$ dependence of the data, we find agreement with a quark-parton picture, namely the cross sections have a power-law behavior in $1\ensuremath{-}x$ independent of ${p}_{\mathrm{beam}}$ and ${p}_{t}$.