Nellie's soccer team is having a great season. The team is being coached by Nellie's mom, who divided the team into five groups: 1/2 the players are forwards, 1/6 are wings, 1/6 are halfbacks, 1/12 are fullbacks, and 2 others are goalies. How many players are on Nellie's team, and how many are in each group?
To find the number of players on Nellie's team and the number of players in each group, we need to combine the fractions and solve for the total number of players.
Let's calculate the total fraction of players for each group:
Forwards: 1/2
Wings: 1/6
Halfbacks: 1/6
Fullbacks: 1/12
Now, we sum up the fractions:
1/2 + 1/6 + 1/6 + 1/12 = 6/12 + 2/12 + 2/12 + 1/12 = 11/12
The fraction 11/12 represents the total number of players on the team. Since we know that there are also 2 goalies, we add them to conclude that the fraction 11/12 represents the whole team.
To find the number of players in each group, we need to divide the total number of players (11/12) by each group's fraction:
Forwards: (1/2) / (11/12) = (1/2) * (12/11) = 6/11
Wings: (1/6) / (11/12) = (1/6) * (12/11) = 2/11
Halfbacks: (1/6) / (11/12) = (1/6) * (12/11) = 2/11
Fullbacks: (1/12) / (11/12) = (1/12) * (12/11) = 1/11
Since the fraction 11/12 represents the whole team, we need to find the actual number of players in each group. To do this, we multiply the fractions with the total number of players on the team (11/12):
Forwards: (6/11) * 11 = 6 players
Wings: (2/11) * 11 = 2 players
Halfbacks: (2/11) * 11 = 2 players
Fullbacks: (1/11) * 11 = 1 player
Goalies: 2 players
Therefore, Nellie's soccer team has a total of:
Forwards: 6 players
Wings: 2 players
Halfbacks: 2 players
Fullbacks: 1 player
Goalies: 2 players
24
gfnregt
Let x = total players
1/2 x + 1/6 x + 1/6 x + 1/12 x = x - 2
Get common denominator.
6/12 x + 2/12 x + 2/12 x + 1/12 x = x - 2
Add like terms.
11/12 x = x - 2
Multiply both sides by 12.
11x = 12x - 24
You should be able to take it from there. I hope this helps.