The statement modeled by the expression \( \frac{100}{p} \) is:
The coach received 100 tokens for the amusement park rides. If there are \( p \) players on the team, each player will receive \(\frac{100}{p}\) tokens.
This is because the expression \(\frac{100}{p}\) represents the total number of tokens (100) divided by the number of players (p), giving the number of tokens each player would receive.