#### Answer

$p=56$

#### Work Step by Step

We start with the given equation: $\frac{5}{7}p-10=30$
We add $10$ to both sides of the equation and combine like terms: $$\frac{5}{7}p-10+10=30+10$$$$\frac{5}{7}p=40$$
We multiply by $\frac{7}{5}$, the reciprocal of $\frac{5}{7}$, on each side of the equation: $$\frac{7}{5}\times\frac{5}{7}p=\frac{7}{5}\times40$$$$p=56$$