Each person in an IT department of 25 people works on at least one of 3 major projects: system security, program implementation, platform development. 10 people work on system security, 13 work on program implementation, and 12 work on platform development. 4 people work on system security and platform development, 5 people work on program implementation and platform development, and 2 people work on all three projects. How many people work on system security and program implementation?

Question

Mathematics

Beau

6 November, 22:19

Each person in an IT department of 25 people works on at least one of 3 major projects: system security, program implementation, platform development. 10 people work on system security, 13 work on program implementation, and 12 work on platform development. 4 people work on system security and platform development, 5 people work on program implementation and platform development, and 2 people work on all three projects. How many people work on system security and program implementation?

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Answers (1)

Know the Answer?

Donavan Ross · Answer 1

3

Step-by-step explanation:

Let system security be A, program implementation be B and platform development be C

Then:

25 = A + B + C - AB - BC - AC + ABC

where AB is system security and program implementation,

BC is program implementation and platform development,

AC is system security and platform development and

ABC is all three

So plug in the given numbers to get:

25 = 10 + 13 + 12 - AB - 5 - 4 + 2

25 = 35 - AB - 9 + 2

25 = 35 - AB - 7

AB = 35 - 7 - 25

AB = 3