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Each of the 30 boxes in a certain shipment with either 10

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Each of the 30 boxes in a certain shipment with either 10 [#permalink] New post 09 Nov 2008, 19:13
Each of the 30 boxes in a certain shipment with either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?

A. 4
B. 6
C. 10
D. 20
E. 24
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Re: boxes--28 [#permalink] New post 09 Nov 2008, 20:18
petercao wrote:
Each of the 30 boxes in a certain shipment with either 10 pounds or 20 pounds, and the average (arithmetic mean) weight of the boxes in the shipment is 18 pounds. If the average weight of the boxes in the shipment is to be reduced to 14 pounds by removing some of the 20-pound boxes, how many 20-pound boxes must be removed?

A. 4
B. 6
C. 10
D. 20
E. 24


(10x+20y)/(x+y)=18
x+y=30
x=6,y=24

(10*6+20z)/(6+z)=14
z=4

24-4=20

D
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Re: boxes--28 [#permalink] New post 10 Nov 2008, 00:05
D.
echo the same explanation:

10x+20y=540==> 2z+y=54--(1)

x+y=30----(2)

x=6, y=24

60+ 20z=14(6+z)
=> z=4.

so 24-4=20 boxes were removed.
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Re: boxes--28 [#permalink] New post 10 Nov 2008, 03:21
D with a different way of computing.

540 - 20x = 14(30 - x)
x = 20.
Re: boxes--28   [#permalink] 10 Nov 2008, 03:21
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