There are 566 members in arts club and 522 are members in the music club. If the total number of people who are members in either or both the clubs is 963, how many people are members in both clubs?

Question

Genesis Allen · Accepted Answer

See a solution process below:

The total membership of both clubs, with overlap, is: #566 + 522 = 1088# However, without overlap we are told the are a total of 963 in the clubs. We can find the total number in both by subtracting the total number of individual members from the total number of members with overlap we calculated above: #1088 - 963 = 125# There are 125 people who are members of both clubs.

Hazel Anglin · Answer

#125#

This can be done with Set Theory, but I will stick with the traditional method.

The number of members in either or both the clubs #= 963#.

The number of members in the arts club #= 566#.

Therefore, The number of members in only music club is #= (963 - 566) = 397#

The number of members in the music club is #= 522#.

Therefore, the number of members of both clubs #= (522 - 397) = 125#.

Hope this helps.

Savannah Anderson · Answer

undefined To find the number of people who are members in both clubs, we can use the principle of inclusion and exclusion.

Total members in both clubs = Total members in arts club + Total members in music club - Total members in either club

Total members in both clubs = 566 + 522 - 963
Total members in both clubs = 1085 - 963
Total members in both clubs = 122.

So, there are 122 people who are members in both the arts and music clubs.