Answer:
1. 2 ≤ n ≤ 4
2. 4 * 20
3. T < 80
4. (2 * 4) + (4 * 3)
5. 16 ≤ P ≤ 32
Note: The quantities described are as follows:
1) the allowable number of players on a team
2) the number of points, , Han's team earns in one round if every player earns a perfect score
3) the number of points, , Han's team earns in one round if no players earn a perfect score
4) the number of players, , in a game with six teams of different sizes: two teams have 4 players each and the rest have 3 players each
5) the possible number of players in a game with eight teams
Step-by-step explanation:
1. Let the number of players be n
Since each team can have between 2 and 4 players
n ≥ 2 or 2 ≤ n, and n ≤ 2
Therefore, the allowable number of players on a team
is given by 2 ≤ n ≤ 4
2) There are four players in Han's team and a perfect score is 20
Therefore, the number of points Han's team earns in one round if every player earns a perfect score is given by 4 * 20
3) There are four players in Han's team
Total score if each player in Han's team earns a perfect score is 4 * 20 = 80
Let the total score of Han's team be T
Therefore, the number of points, Han's team earns in one round if no players earn a perfect score is given by T < 80
4) If two team have 4 players, it is given by 2 * 4
If the rest four teams have 3 players each, it is given by 4 * 3
Therefore, the number of players in a game with six teams of different sizes: two teams have 4 players each and the rest have 3 players each is given by (2 * 4) + (4 * 3)
5) Let the possible number of players in a game with be P
Maximum number of players in eight teams = 4 * 8 = 32
Minimum number of players in eight teams = 2 * 8 = 16
P ≤ 32 and P ≥ 16 or 16 ≤P
Therefore, the possible number of players in a game with eight teams is given by 16 ≤ P ≤ 32
, then collect like terms