Question

Enter the value of p so the expression 5/6-1/3nis equivalent to p(5-2n).

Answer 1

Solution:

We are given that

$\frac{5}{6} - \frac{1}{3}n = p(5-2n) \\ \frac{5}{6} - \frac{1}{3}n = 5p-2pn$

By our initial condition, 5p = $\frac{5}{6}$ while -2pn = $-\frac{1}{3}$. 

$5p = \frac{5}{ \frac{6}{5}} = \frac{5}{30}\\ p = \frac{1}{6} \\ \\ -2pn = -\frac{1}{3}n \\ p= \frac{1}{ \frac{3}{2}} = \frac{1}{6}$

and we are done as $\frac{5}{6} - \frac{1}{3}n = p(5-2n)$ ⇒ $\frac{5}{6} - \frac{1}{3}n = \frac{5}{6} - \frac{1}{3}n$