SOLUTION: 500 students are enrolled in at least two of these three classes: Math, English, and History. 170 are enrolled in both Math and English, 150 are enrolled in both History and Engl

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Question 174555: 500 students are enrolled in at least two of these three classes: Math, English, and History. 170 are enrolled in both Math and English, 150 are enrolled in both History and English, and 300 are enrolled in Math and History. How many of the 500 students are enrolled in all three?

Answer by rapaljer(4551) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = number of students enrolled in all three classes. Since students are enrolled in at least two classes, there are four categories of students summarized below.

x= Students in all three classes
170 -x = students in math and English but not history
150 - x = students in English and history but not math
300 - x = students in history and math but not English

The sum of these students must equal 500.
x + 170-x + 150-x + 300-x = 500
620-2x = 500
-2x = -120
x=60

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