500 people are enrolled in at least two of these three classes: art, drama, and piano. 170 are enrolled in both art and drama, 150 are enrolled in both piano and drama, and 300 are enrolled in art and piano. How many of the 500 people are enrolled in all three?

Question

Mathematics

Dario Stein

11 September, 14:24

500 people are enrolled in at least two of these three classes: art, drama, and piano. 170 are enrolled in both art and drama, 150 are enrolled in both piano and drama, and 300 are enrolled in art and piano. How many of the 500 people are enrolled in all three?

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Answers (1)

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Ducky · Answer 1

Answer: 60

Step-by-step explanation:

let x="students enrolled in all three"

"170 are enrolled in both Math and English" __ so 170-x are enrolled in ONLY Math and English

"150 are enrolled in both History and English" __ so 150-x are enrolled in ONLY History and English

"300 are enrolled in Math and History" __ so 300-x are enrolled in ONLY Math and History

"500 students are enrolled in at least two of these three classes"

so (170-x) + (150-x) + (300-x) + x = 500

620-2x=500

120=2x

60=x