In a school orchestra, there are 36 violinists, 48 cellists, and 60 flutists. If the conductor wants to create small ensembles where each ensemble has an equal number of the same type of instrument, what is the maximum number of musicians that can be in each ensemble?
Question
In a school orchestra, there are 36 violinists, 48 cellists, and 60 flutists. If the conductor wants to create small ensembles where each ensemble has an equal number of the same type of instrument, what is the maximum number of musicians that can be in each ensemble?
Solution
To solve this problem, we need to find the greatest common divisor (GCD) of the numbers 36, 48, and 60. The GCD is the largest number that can divide each of the numbers without leaving a remainder.
Here are the steps:
-
First, let's find the factors of each number:
- The factors of 36 are: 1, 2, 3, 4, 6, 9, 12, 18, 36
- The factors of 48 are: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48
- The factors of 60 are: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
-
Next, let's find the common factors of these three numbers:
- The common factors are: 1, 2, 3, 4, 6, 12
-
The greatest of these common factors is 12.
So, the conductor can create ensembles with a maximum of 12 musicians each, where each ensemble has an equal number of the same type of instrument.
Similar Questions
n a symphony orchestra, there are 2 vacancies for cellists only, 4 vacancies for violinists only and 4 vacancies for any of these musicians. In how many ways can these vacancies be filled from 15 applicants, of whom 7 are violinists and 8 are cellists?
There are 54 students in the orchestra and twice that number in the band. There are 10 boys and 37 girls in the choir. If each student only participates in one group, how many students total are there in the orchestra, the band, and the choir?
How many instrument families are there in orchestra music?Group of answer choicesonefourfivesix
In a drama workshop, there are 6 actors who would like to appear in a scene. However, the scene has only 5 different roles. Each role can be played by anyone, and no actor can play more than one role. How many different casts are possible?
Brenna is getting a band together. There are 10 possible drummers and 2 lead singers to choose from. For the bassist, Brenna has 4 options. How many different bands can Brenna create?
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.