in a survey of 120 people, it was found that 65 read Newsweek magazine, 45 read Time magazine, 42 read Fortune Magazine, 20 read both newsweek and Time, 25 read both newsweek and fortune, 15 read both time and fortune and 8 read all the three magazines. find the number of people who read at least one of the three magazines

This is a problem involving the principle of inclusion-exclusion, which helps to count the number of elements in the union of several sets.

Let:
- \( N \) = number of people who read Newsweek = 65
- \( T \) = number of people who read Time = 45
- \( F \) = number of people who read Fortune = 42
- \( N \cap T \) = number of people who read both Newsweek and Time = 20
- \( N \cap F \) = number of people who read both Newsweek and Fortune = 25
- \( T \cap F \) = number of people who read both Time and Fortune = 15
- \( N \cap T \cap F \) = number of people who read all three magazines = 8

The formula for the number of people who read at least one of the three magazines is:

\[
|N \cup T \cup F| = N + T + F - (N \cap T) - (N \cap F) - (T \cap F) + (N \cap T \cap F)
\]

Now let's plug in the values:

\[
|N \cup T \cup F| = 65 + 45 + 42 - 20 - 25 - 15 + 8
\]

Simplifying:

\[
|N \cup T \cup F| = 152 - 60 + 8 = 100
\]

Thus, the number of people who read at least one of the three magazines is **100**.

Would you like more details or have any questions? Here are five related questions to explore:

1. How many people read only Newsweek?
2. How many people read exactly two magazines?
3. How many people do not read any magazine?
4. How many people read exactly one magazine?
5. How many people read both Newsweek and Time but not Fortune?

**Tip**: Always start with defining sets and relationships clearly when working with inclusion-exclusion problems.

In a survey of 120 people, it was found that 65 read Newsweek magazine, 45 read Time magazine, 42 read Fortune magazine, 20 read both Newsweek and Time, 25 read both Newsweek and Fortune, 15 read both Time and Fortune, and 8 read all three magazines. Find the number of people who read at least one of the three magazines.

Discover how to use the Inclusion-Exclusion Principle to find the number of people who read at least one of Newsweek, Time, or Fortune magazines in a survey of 120 people. This step-by-step guide covers set theory concepts and the inclusion-exclusion formula, perfect for high school students in Grades 10-12.

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