Math Problem Statement
A survey of 245 adults found that during the last year, 65 traveled by plane but not by train, 45 traveled by train but not by plane, 35 traveled by bus but not by plane or by train, 70 traveled by bus and plane, 45 traveled by all three, and 180 traveled by plane or train. How many did not travel by any of these modes of transportation?
Solution
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Math Problem Analysis
Mathematical Concepts
Set Theory
Inclusion-Exclusion Principle
Formulas
Inclusion-Exclusion formula: |A ∪ B ∪ C| = |A| + |B| + |C| - |A ∩ B| - |B ∩ C| - |A ∩ C| + |A ∩ B ∩ C|
Set operations: Union, Intersection, Set Difference
Theorems
Inclusion-Exclusion Principle
Suitable Grade Level
Grades 10-12
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