Questions on Algebra: Numeric Fractions answered by real tutors!

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Question 169681: 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?
: 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?

Answer by Mathtut(1361) About Me  (Show Source):
You can put this solution on YOUR website!
We know from the givens that 2/3 of the students are under grads and 1/3 are grads.
:
now 1/4 of the under grads commute(1/4)(2/3)=2/12=1/6 which is the amount of undergrads that commute--->
of that 1/10 drive more than 40 miles(1/10)(1/6)=1/60undergrads drive more than 40 miles.
:
now 1/3 of the grads commute(1/3)(1/3)=1/9which is the amount of grads that commute----->
of that 1/6 drive more than 40 miles(1/6)(1/9)=1/54grads that drive more than 40 miles.
:
now we only need add the amount of under grads and grads that commute more than 40 miles.....
(1/60)=(1/54)=19/540=.035 so 3.5% of commuters drive more than 40 miles