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?

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)

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