an​ orchestra, 23 people can play stringed​ instruments, 21 can play​ brass, and 15 can play percussion.​ Further, 9 of the performers can play both strings and​ brass, whereas 8 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.)

Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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In an​ orchestra, 23 people can play stringed​ instruments, 21 can play​ brass, and 15 can play percussion.​ Further, 9 of the performers can play both strings and​ brass, whereas 8 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.)

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