Difficult question.

A Soccer team has 180 members. The league consists of 24 eight year olds, 96 nine year olds, and 60 ten year olds. You want to divide the members into teams that have the same number of 8 year olds, 9 year olds, and 10 year olds. What is the greatest number of teams that can be formed? How many 10 year olds are on each team?

 

Maybe I am not understanding :/

 

there is only 24    8 year olds so the biggest number of teams is 24

 

so there will be 24 teams with 1 eight year old, 4 nine year olds and 2 ten year olds 

 

And there will be 12 lonely 10 year olds left over.

Well, there is 11 players on a soccer team    180/11= 16.36  teams.... or 16 whole teams with a few people left over...this is the MAXIMUM

The limiting factor seems to be 8 year olds there is only 24 of them....let'e put two of them on each team  (since there is not enough people for 24 teams)

Each team will have      2 eight year old   (for a total of 24  8 y/o s)  with no leftover 8 y/o's    ... 12 teams

                                      4 nine year olds  (for a total of 48 9 y/o s)     48 left over                          12 teams

                                      5 ten year olds                                                no leftovers

 

12 teams ea   with  2 eight year olds    4 nine year olds  and 5 ten year olds         there will be 48  9 y/o s with no team.....bummer

.....on second thought.....maybe if we put more 9 y/o on the team we can use more people

 

Let's try     16 teams

1 8 y/o

6 9 y/o

4....nope  not enoug 10s

 

15 teams

1  8 y/o

6  9 y/o

nope not enough 10s

14

1 8y/o

6 9 yo

not enough 10s

 

 13

1 8y/o

7  9 y/o

3 10s              Looks like 13 is it    13 teams, not 12

A Soccer team has 180 members. The league consists of 24 eight year olds, 96 nine year olds, and 60 ten year olds. You want to divide the members into teams that have the same number of 8 year olds, 9 year olds, and 10 year olds. What is the greatest number of teams that can be formed? How many 10 year olds are on each team

 

24=2 X 2 X 2 X 3

96=2 X 2 X 2 X 2 X 2 X 3

60=2 X 2 X 3 X 5

GCD=2 X 2 X 3=12

24/12=2 teams of 8-year olds

96/12=8 teams of 9-year olds

60/12=5 teams of 10-year olds.

2 + 8 + 5=15 maximum number of teams

60/15=4 number of 10-year olds on each team.