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 Engli
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Question 174573: 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?
You can put this solution on YOUR website! 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?
:
Let x = no. students enrolled in all three
:
These students are represented in an equal amt in all three groups:
:
The equation for students taking only two subjects
(170-x) + (150-x) + (300-x) = 500 - x
620 - 3x + x = 500
-2x = 500 - 620
-2x = -120
x = +60 students take all three subjects
:
Check solution
170 - 60 = 110 students taking Math & Eng only
150 - 60 = 90 students taking Hist & Eng only
300 - 60 = 240 students taking Math & Hist only
All 3 sub = 60 students
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Tot stud =500
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