SOLUTION: 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 m

Question 36192: 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 twicde as many undergraduate students as there are graduate students, then what fraction of the commuters drive more than 40 miles daily?
Answer by mukhopadhyay(490) (Show Source): You can put this solution on YOUR website!
Number of graduate students = x
Number of undergraduate students = 2x
Based on the question:
Number of graduate students who commute = x/3
Number of undergraduate students who commute = 2x/4 = x/2
Total commuters = x/3+x/2 = 5x/6.
Number of graduate students driving above 40 miles = x/6
Number of undergraduate students driving above 40 miles = 2x/10 = x/5
Total number of students driving above 40 miles = x/6 + x/5 = 11x/30.
If y fraction of the commuters drive more than 40 miles daily,
y*(Total commuters) = Population driving over 40 miles.
So, y*(5x/6) = 11x/30
=> y = (11x/30)(6/5x) = (11*6)/(30*5) = 11/25
Answer: 11/25

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