Answer:
Yes, everyone who has signed up will have a spot on a 3-player team.
Step-by-step explanation:
If there are 114 people signed up to play in a basketball tournament, and each team consists of 3 players, we can determine how many teams can be formed and whether everyone will have a spot on a team.
The number of teams (
) is given by dividing the total number of people by the number of players per team:



So, there are 38 teams that can be formed. However, since each team consists of 3 players, the total number of players on all teams is
, which is equal to the total number of people signed up.
Therefore, everyone who has signed up will have a spot on a 3-player team, and there will be no one left without a team. Each person will be part of a team in the basketball tournament.