Question

6. In a video game, players form teams and work together to earn as manypoints as possible for their team. Each team can have between 2 and 4players. Each player can score up to 20 points in each round of thegame. Hanand three of his friends decided to form a team and play a round.6. Write an expression, an equation, or an inequality for each quantitydescribed here. If you use a variable, specify what it represents.6a. the allowable number of players on a team66. the number of points Han's team earns in one round if every playerearns a perfect score6c, the number of points Han's team earns in one round if no players earna perfect score

Answer 1

`\begin{gathered} a)2\le x\le4 \\ b)p=80 \\ c)p\le76 \end{gathered}`

Step-by-step explanation

a) Let the allowable number of players in each team be x.

Each team can have between 2 and 4 players. This means that the minimum number of players is 2 and the maximum number of players is 4.

Therefore, the inequality that represents the allowable number of players in each team is:

`\begin{gathered} x\ge2 \\ x\le4 \\ \Rightarrow2\le x\le4 \end{gathered}`

b) To earn a perfect score, a player must have 20 points. If the four players in Han's team have perfect points, it means that each player has 20 points.

Let the number of points scored be p.

Therefore, the number of points Han's team earns in one round if each player earns a perfect score is:

`\begin{gathered} p=20\cdot4 \\ p=80 \end{gathered}`

c) If no player in Han's team earns a perfect score, then, each player's score must be less than 20 points. Therefore, each player can earn as much as 19 points.

Therefore, 4 players can earn up to:

`\begin{gathered} 4\cdot19 \\ 76 \end{gathered}`

In other words, the team can earn up to 76 points.

Hence, the inequality that represents the number of points earned in one round if no players earn a perfect score is:

`p\le76`