Given the equations: $p=q+4$, $r=2q-1$, and $p+r=50$. Solve for the exact values of: $q$, $p$, and $r$.

$q=15$, $p=19$, $r=29$

$q=\frac{47}{3}$, $p=\frac{59}{3}$, $r=\frac{91}{3}$

$q=16$, $p=20$, $r=31$

$q=47$, $p=51$, $r=93$