SOLUTION: I need help with this word problem, please. At a well-known university, 1/4 of the undergraduate students commute, and 1/3 of the graduate students commute. One-ten

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Question 295321: I need help with this word problem, 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?
Answer by ankor@dixie-net.com(22740) About Me  (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?
:
Let's use a convenient number for the total students: 720 has a lot of factors
:
It says,"there are twice as many undergrads as there are grad students,"
That would give us us 480 undergrads, and 240 grads
:
1/4 of the undergraduates commute;
1%2F4 * 480 = 120
:
1/3 of the graduates commute.
1%2F3 * 240 = 80
:
1/10 of the undergraduates drive more than 40 miles daily
1%2F10 * 480 = 48
:
1/6 of the graduates drive more than 40 miles daily.
1%2F6 * 240 = 40
:
what fraction of the commuters drive more than 40 miles daily?
Total commuters: 120 + 80 = 200
Total commuters drive more than 40 mi: 48 + 40 = 88
:
Then: 88%2F200 = 11%2F25 of the commuters commute over 40 mi