SOLUTION: 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 da

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Question 77384: 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):
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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 x = number of grads
It says
"there are twice as many undergraduate students as there are graduate students"
Then 2x = number of undergrads
:
Write an expression for each phrase
:
"1/4 of the undergraduate students commute,"
(1/4)2x
(2/4)x
:
"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
(2/10)x
:
"1/6 of the graduate students drive more than 40 miles daily."
(1/6)x
:
"what fraction of the commuters drive more than 40 miles daily?"
:
total commuters
(2/4)x + (1/3)x
(6/12)x + (4/12)x = (10/12)x
:
total commuters > 40 mi:
(2/10)x + (1/6)x)
(6/30)x + (5/30)x = 11/30x
:
Faction of commuters >40 mi= (11/30)x / (10/12)x
:
WE can cancel out x and just deal with the two fractions:
:
11%2F30 * 12%2F10%29 = 132%2F300 = 11%2F25 commute > 40
:
:
I hope all this made sense to you.