Question

A recreation center holds a soccer game every Saturday morning for older teens. The group agreed that there should be at least five players on each team. One team started out with 17 players. After an hour of playing three players started leaving every 5 minutes. For at least how long can the team keep playing?

Answer 1

The soccer team can keep playing for at least 20 minutes before the number of players drops below the minimum required five players.

Step-by-step explanation:

A team with 17 players starts playing soccer and three players leave every 5 minutes. To find out for how long the team can keep playing with at least five players on the team, we perform the following calculation:

Initially, the team has 17 players.

After every 5 minutes, the team loses 3 players.

To reach the minimum of 5 players, we need to see how many groups of 3 can be subtracted from 17 until we reach 5 or fewer players.

To solve this, we subtract multiples of 3 from 17 until we reach a number that is 5 or above but where the next subtraction would drop us below 5.

17 - 3 = 14 (after 5 minutes)

14 - 3 = 11 (after 10 minutes)

11 - 3 = 8 (after 15 minutes)

8 - 3 = 5 (after 20 minutes)

So, after 20 minutes, the team would be left with exactly 5 players, which is the minimum to keep playing. Therefore, three players could leave at 25 minutes and the team would not be able to keep playing as they would drop below the minimum. Hence, the team can play for at least 20 minutes before they have fewer than 5 players.