How do you get 34 from p = 5s - (100 + 2s) when p = 0 is s ≈ 33.333.

P = 5s - (100 + 2s)           Carefully remove the brackets. Watch the signs.
P = 5s - 100 - 2s
P = 3s - 100

0 = 3s - 100 Add 100 to both sides.
100 = 3s Divide by 3
100/3 = s

s = 33.33333  It is just a rounding factor. It depends on what you are really finding. So whatever answers you're given (if any), choose the one closest to 33.33333 which is likely what you got when you did it.