Question 88200: Hi, I have a word problem that I need help with please.
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? Thank you!!
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! 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?
:
It says there are twice as many undergrad as grads, using this information:
Let x = no. of grad students
Then 2x = no. of undergrad students
Then x + 2x = 3x = total number of student
:
1/4 of the undergraduate students commute,
(1/4)*2x = (1/2)x
:
and 1/3 of the graduate students commute.
(1/3)x
:
One-tenth of the undergraduate students drive more than 40 miles daily
(1/10)*2x = (1/5)x
:
and 1/6 of the graduate students drive more than 40 miles daily.
(1/6)x
:
then what fraction of the commuters drive more than 40 miles daily?
Total number of commuters:
(1/2)x + (1/3)x =
(3/6)x + (2/6)x = (5/6)x; number of commuters
:
Total number of over 40 mi students
(1/5)x + (1/6)x =
(6/30)x + (5/30)x = (11/30)x: number of over 40
:
What fraction of total commuters are over 40 commuters?
For convenience let x = 120
(5/6)*120 = 100 students commute
(11/30) * 120 = 44 students over 40
:
44/100 = 44% of the commuters, are over 40 mi commuters
;
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