Question

a recreation center holds a soccer game every saturday morningagreed that there should be at least 5 players on each team. One team started out with 17 players. After an hour of playing, 3 players started leaving every 5 minutes. At most, for how long can the team keep playing?

Answer 1

Given the scenario where a soccer team starts with 17 players and loses 3 every 5 minutes, by calculating the number of 5-minute intervals before the team has fewer than 5 players, the team can keep playing for at most 20 minutes.

Step-by-step explanation:

The student's question relates to how long a soccer team can keep playing given a certain situation. The team starts with 17 players and loses 3 players every 5 minutes, with the requirement that there must be at least 5 players on each team for the game to continue.

To solve this, we can set up a sequence that represents the number of players left after every 5 minutes. Starting with 17 players, losing 3 every 5 minutes, after 'n' intervals of 5 minutes, the number of players left will be:

Remaining players

= 17 - 3n
The team can keep playing as long as there are at least 5 players, so we need to find the largest 'n' for which the remaining players are ≥5:

5 ≤ 17 - 3n

By rearranging this inequality, we can solve for 'n':

1. Add 3n to both sides: 3n + 5 ≤ 17
2. Subtract 5 from both sides: 3n ≤ 12
3. Divide both sides by 3: n ≤ 4

Since 'n' represents the number of 5-minute intervals, the team can keep playing for 4 intervals of 5 minutes each, which is equivalent to 20 minutes. Therefore, the team can keep playing for at most 20 minutes before dropping below the required minimum number of players.