Question

1. The music department needs to secure buses for a field trip. Listed below are the total number of participants in each of the band, choir and orchestra. Use a Venn Diagram to solve the problem. 60 students play in the band. 70 students sing in the choir. 50 students play in the orchestra. 12 students are in the band and orchestra. 10 students are in the band and choir. 5 students are in the choir and orchestra 3 students are in the band, choir, and orchestra How many students participated only in the choir? How many students participated only in the band? How many students participated only in orchastra?
PLS HELP

Answer 1

The number of students who participated in Band and Orchestra only according to the Venn diagram are 41 and 36 students respectively.

Let :

• Number of students in band = B
• Number of students in Orchestra = O
• Number of students in Choir = C

• BnOnC= 3
• (CnO) only = 5 - 3 = 2
• (BnC) only = 10 - 3 = 7
• (BnO) only = 12 - 3 = 9

• Number of students in Band only = (60 - (9+3+7)) = 41
• Number of students in Orchestra only = (50 - (9 + 3 + 2) = 36

Therefore, 41 students participated in Band only while 36 students participated in orchestra only.

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