Step 1 :Given the equation: $p = \frac{3(s+100)}{4}$
Step 2 :Solve for $s$ by multiplying both sides by 4: $4p = 3(s+100)$
Step 3 :Distribute the 3: $4p = 3s + 300$
Step 4 :Subtract 300 from both sides: $4p - 300 = 3s$
Step 5 :Divide both sides by 3: $s = \frac{4p - 300}{3}$
Step 6 :\boxed{s = \frac{4p - 300}{3}}$