How many attendees are at a convention if 150 of the attendees are neither female nor students, one-sixth of the attendees are female students, two-thirds of the attendees are female, and one-third of the attendees are students?

Question

Ashly Turner

Computers & Technology

27 September, 17:33

How many attendees are at a convention if 150 of the attendees are neither female nor students, one-sixth of the attendees are female students, two-thirds of the attendees are female, and one-third of the attendees are students?

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Answers (1)

Know the Answer?

Harper Chung · Answer 1

900

Explanation:

Let x be no. of attendees.

No. of students = x/3

No. of female students = x/6 = (1/2) (x/3) = (1/2) no. of students

This implies (1/2) of students are male. So,

No of male students = (1/2) (x/3) = x/6 ... eq (1)

No. of female attendees = 2x/3

No of male attendees = x - (2x/3) = x/3 ... eq (2)

Using eq (1) and eq (2)

No of male non-student attendees = (x/3) - (x/6) = x/6 ... eq (3)

No of male non-student attendees = 150 (Given in question) ... eq (4)

Using eq (3) and eq (4)

=> x/6=150

=> x=150*6

=> x=900 (Answer)