Question

At the annual music festival, the number of Bayview Middle School students competing in the band, chorus, and orchestra competitions is 14, 13, and 17 students respectively. 4 students will compete in all three competitions. 5 students will compete in band and chorus competitions. 6 students will compete in band and orchestra competitions. 7 students will compete in the chorus and orchestra competitions. How many students from Bayview Middle School competed in the music festival

Answer 1

30 students

Explanation:

The problem above can be solved using a Venn diagram :

Using the information given :

The number of students competing :

Band and chorus only (BnC) only = 5 - 4 = 1

Band and Orchestra (BnO) only = 6 - 4 = 2

Chorus and Orchestra (CnO) only = 7-4 = 3

Chorus only (C) = 13 - (1+4+3) = 5

Band only (B) = 14 - (1+4+2) = 7

Orchestra only (O) = 17 - (2+4+3) = 8

The Total Number of Bayview students who competed :

(8+7+5+3+2+1+4) = 30