In a trivia contest, players form teams and work together to earn as many points as possible for their team. Each team can have between 3 and 5 players. Each player can score up to 10 points in each round of the game. Elena and four of her friends decided to form a team and play a round.

Write an expression, an equation, or an inequality for each quantity described here. If you use a variable, specify what it represents.

1. the number of points that Elena's team earns in one round

2. the number of points Elena's team earns if each player misses one point

3. the number of players in a game if there are at least 3 teams

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Ritz01 Ritz01 · Answer 1 · 2020-10-26T01:22:45+01:00

Answer:

(i) From 0 to 50.

(ii) From 3 to 5.

(iii) From 3R to 5R, where R=3,4,5,...

Step-by-step explanation:

Let N be the number of players in a team.

As each team can have numbers of player ranging from 3 to 5, so

[tex]3\leqN\leq5\cdots(i)[/tex]

Let P be the points scored by one player in one round of the game.

As each player can score up to 10 points in each round of the game, so

[tex]0\leq P \leq 10\cdots(ii)[/tex]

(1) There are 5 members in the team formed by Elena.

So, points earned by 5 players in 1 round = 5P

From equation (ii), the range is

[tex]0\leq 5P \leq 50[/tex]

Hence, the points earned by Elena's team is ranging from 0 to 50.

(2) If each played misses 1 point, then,

Points earned by 1 player in 1 round = 10-1=9

Hence, points earned by 5 players in 1 round = 9x5=45.

(3) Let R (an integer) denoted the number of teams.

As there are at least 3 teams in the game, so

[tex]R\geq3\cdots(iii)[/tex]

As the number of players in one team is N, so

the number of players in R team is NR, where R=3,4,5,...

Now, from equation (i)

[tex]3R\leqNR\leq5R[/tex]

Hence, if there are at least 3 teams, then the number of players is ranging from 3R to 5R.

For R=3, the number of players in the game is ranging from 3x3=9 to 5x3=15.