Answer
$p = \frac{248}{35}$
Work Step by Step
$p + 3(\frac{1}{4}p-4) = \frac{2}{5}$
$p + 3(\frac{p}{4}-4) = \frac{2}{5}$
$p + \frac{3p}{4}-12= \frac{2}{5}$
$4p + 3p - 4(12) = 4(\frac{2}{5})$
$7p - 48 = \frac{8}{5}$
$5(7p) - 5(48) = 8$
$35p - 240 = 8$
$35p - 240 - 8 = 0$
$35p - 248 = 0$
$35p = 248$
$p = \frac{248}{35}$
Check:
$\frac{248}{35} + 3(\frac{1}{4}(\frac{248}{35})-4) \overset{?}{=} \frac{2}{5}$
$\frac{248}{35} + 3(-\frac{78}{35}) \overset{?}{=} \frac{2}{5}$
$\frac{248}{35} -\frac{234}{35} \overset{?}{=} \frac{2}{5}$
$\frac{14}{35} \overset{?}{=} \frac{2}{5}$
$\frac{2}{5} = \frac{2}{5}$
