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Commuting students. At a well-known university, 1/4 of the undergraduate students commute, and 1/3 of the graduate students commute. One-tenth of the undergraduate students
drive more than 40 miles daily, and 1/6
of the graduate students drive more than 40 miles daily. If there are twice
as many undergraduate students as there are graduate students, then what fraction of the commuters drive more
than 40 miles daily?

  • Algebra -

    number of grad students = x
    number of undergrads = 2x
    grads more than 40 miles = x/6
    undergrads over 40 miles = 2x/10
    total over 40 miles = 11x/30

    undergrads commuting = 2x/4
    grads commuting = x/3
    total commuting = 5x/6

    fraction of commuters over 40 miles = (11x/30)÷(5x/6) = 1/25

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