Question

A high school swim team has 12 new female swimmers and 30 returning female swimmers. Each practice team must have the same number of new a returning female swimmers.

A) What is the greatest number of practice teams the coach can make using every swimmer?

B) How many new and returning female swimmers will be on each practice team?

Answer 1

Number of new female swimmers is 12 and number of returning female swimmers is 30.

A) As each practice team must have the same number of new and returning female swimmers, so for finding the greatest number of practice teams, we just need to find the GCF(greatest common factor) of 12 and 30.

`12 = 2*2*3\\ \\ 30= 2*3*5`

As the common factors are 2 and 3 , so the GCF will be:
`2*3=6`

Thus, the greatest number of practice teams the coach can make using every swimmer will be 6.

B) As there are total 6 practice teams, so in each team.....

Number of new female swimmers
`=(12)/(6)=2` and

Number of returning female swimmers
`=(30)/(6)=5`