Question

The brass section in a marching band has 24 trombone players and 56 trumpet players. The band director wants to arrange them into equal rows that have as many musicians as possible. However, all of the musicians in each row must play the same instrument. How many rows will there be?

Answer 1

Highest common factor of 24 and 56 is 8, 24+56 is 80, 80 over 8 is 10 rows

Answer 2

10 rows.

Explanation:

In the given problem, "as many musicians as possible" expresses the greatest common factor.

In this case, the greatest common factor between 24 and 56 is 8, because that's the higher factor that can give 24 and 56 from a product, specifically, 3(8) = 24 and 7(8) = 56.

So, if we divide each number by the greatest common factor, we would have

`(24)/(8)=3\\(56)/(8)=7`

That is, there would be 3 rows of trombone players, and 7 rows of trumpet players. In total, there will be 10 rows where in each rows musicians play the same instrument.