8. 100 companies are competing to win a coveted government contract. There are three re- quirements, A, B, and C, that the government has set. We have the following breakdown of the companies in terms of satisfying the requirements: • The total number of companies satisfying requirement A is 31. • The total number of companies satisfying requirement B is 65. • The total number of companies satisfying requirement C is 44. • The total number of companies satisfying requirements A and B is 17. • The total number of companies satisfying requirements A and C is 15. • The total number of companies satisfying requirements C and B is 18. How many companies satisfy all three requirements?

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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8. 100 companies are competing to win a coveted government contract. There are three re-
quirements, A, B, and C, that the government has set. We have the following breakdown of
the companies in terms of satisfying the requirements:
• The total number of companies satisfying requirement A is 31.
• The total number of companies satisfying requirement B is 65.
• The total number of companies satisfying requirement C is 44.
• The total number of companies satisfying requirements A and B is 17.
• The total number of companies satisfying requirements A and C is 15.
• The total number of companies satisfying requirements C and B is 18.
How many companies satisfy all three requirements?
Transcribed Image Text:8. 100 companies are competing to win a coveted government contract. There are three re- quirements, A, B, and C, that the government has set. We have the following breakdown of the companies in terms of satisfying the requirements: • The total number of companies satisfying requirement A is 31. • The total number of companies satisfying requirement B is 65. • The total number of companies satisfying requirement C is 44. • The total number of companies satisfying requirements A and B is 17. • The total number of companies satisfying requirements A and C is 15. • The total number of companies satisfying requirements C and B is 18. How many companies satisfy all three requirements?
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