Solution:
We are given that
[tex] \frac{5}{6} - \frac{1}{3}n = p(5-2n) \\ \frac{5}{6} - \frac{1}{3}n = 5p-2pn[/tex]
By our initial condition, 5p = [tex]\frac{5}{6}[/tex] while -2pn = [tex]-\frac{1}{3}[/tex].
[tex]5p = \frac{5}{ \frac{6}{5}} = \frac{5}{30}\\ p = \frac{1}{6} \\ \\ -2pn = -\frac{1}{3}n \\ p= \frac{1}{ \frac{3}{2}} = \frac{1}{6} [/tex]
and we are done as [tex] \frac{5}{6} - \frac{1}{3}n = p(5-2n)[/tex] ⇒ [tex]\frac{5}{6} - \frac{1}{3}n = \frac{5}{6} - \frac{1}{3}n[/tex]
