Question

in a video game, players form teams and work together to earn as many points as possible for their team. each team can have between 2 and 4 players. each player can score up to 20 points in each round of the game. han and three of his friends decided to form a team and play a round. match each expression or inequality to the quantity that it represents.

• the allowable number of players on a team
• the number of points hans team earns in one round if every player earns a perfect score
• the number of points hans team earns in one round if no players earn a perfect score
• 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
• the possible number of players in a game with eight teams

p≥2 and ≤4 (or 2≤p<4), where p is the number of players on a team

s<80, where s is the score of the team

t≤30 (or 15≤t), where t is the total number of players in a game

2(4)+4(3)

4(20)

Explanation:

Step1: Calculate number of players in a game

There are eight - teams with 4 players each and six - teams with 3 players each. So the total number of players $T$ in a game is calculated as $T=8\times4 + 6\times3$.
$T = 32+18=50$.

Step2: Determine the number of players on a team

The number of players $p$ on a team satisfies $2\leq p\leq4$.

Step3: Calculate total score limit

The total score $S$ of a team has the limit $S < 80$.

Step4: Analyze Han's team points

If every player earns a perfect score, and assume the number of players on Han's team is $p$ and each player can score up to 20 points, the number of points $P$ Han's team earns in one round if every player earns a perfect score is $P = 20p$. Since $2\leq p\leq4$, then $40\leq P\leq80$. But since $S < 80$, when $p = 4$, $P=20\times4 = 80$ is not allowed. So the maximum value of $p$ for Han's team to get a non - exceeding score when all players get perfect scores is $p = 3$. And the number of points Han's team earns in one round if every player earns a perfect score is $20\times3=60$.

Answer:

• The possible number of players in a game: $T = 50$.
• The number of players on a team: $2\leq p\leq4$.
• The score limit of a team: $S < 80$.
• The number of points Han's team earns in one round if every player earns a perfect score: When $p = 3$, the number of points is $60$.