In an orchestra, 25 people can play stringed instruments, 21

Last updated: 7/14/2022

In an orchestra, 25 people can play stringed instruments, 21 can play brass, and 12 can play percussion. Further, 9 of the performers can play both strings and brass, whereas 4 can play both strings and percussion. If no one can play all three types of instruments, what are the maximum and minimum numbers of people in the orchestra? (Hint: Consider expressing the numbers in some of the regions of your diagram in terms of a single unknown, say x.)