At a well-known university 1/4 of the undergraduate students commute, and 1/3 of the graduate students commute. 1/10 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?
2007-05-02 15:58:02 · 5 answers · asked by spoons 1 in Science & Mathematics ➔ Mathematics
Let n = number of students
2n/3 = # of undergrads
n/3 = # of grads
2n/12 + n/9 = (6n + 4n)/36 = 5n/18 commute
2n/30 + n/18 = (6n + 5n)/90 = 11n/90 commute more than 40 miles, so
(11n/90)(18/5n) = 11/25 of the commuters commute more than 40 miles.
2007-05-02 16:45:50 · answer #1 · answered by Helmut 7 · 0⤊ 0⤋
We are given the following : "there are twice as many undergraduate students as there are graduate students" -- so U(ndergrads) = 2*G(rads), so for the rest of the exercise, we substitute "2*G" for the number of Undergrads.
Now, "1/4 of the undergraduate students commute" and we already know that U(ndergrads) = 2*G so 1/4 of 2*G = 1/2 G undergrads commute.
"... and 1/3 of the graduate students commute" so 1/3 G grads commute.
So the total number of commuters is: 1/2 G + 1/3 G = 5/6 G
Additionally,
"1/10 of the undergraduate students drive more than 40 miles daily" ... so 1/10 of 2*G = 1/5 G undergrads drive far.
"and 1/6 of the graduate students drive more than 40 miles daily" ... so 1/6 G grads drive far.
So the total number of far commuters is: 1/5 G + 1/6 G = 11/30 G
The fraction of commuters who drive more than 40 miles is (# of far commuters ) / (# of commuters) = (11/30 G) / (5/6 G) = (11/30) / (5/6) = (11/30) * (6/5) = (11*6) / (30*5) = (11*1) / (5*5) = 11/25 of commuters are far commuters.
2007-05-02 17:26:30 · answer #2 · answered by Truly W 5 · 0⤊ 0⤋
Take a hypothetical university with 7200 students.
4800 are undergrads. 1200 of them commute. 480 drive more than 40 miles/day. The corresponding figures with the grads is 2400, 800, and 400. So 880 of the 2000 commuters drive more than 40 miles/day, or 11/25th of the commuters.
2007-05-02 16:07:52 · answer #3 · answered by cattbarf 7 · 0⤊ 0⤋
11/25, as stated above.
This is great GRE prep work!
2007-05-02 16:08:51 · answer #4 · answered by Steve B 2 · 0⤊ 0⤋
pay attention in class and do your own homework!
2007-05-02 16:05:34 · answer #5 · answered by vtown_german 3 · 0⤊ 0⤋