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

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VP
Joined: 22 Nov 2007
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Each of the 30 boxes in a certain shipment with either 10 [#permalink]  12 Jan 2008, 04:22
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
SVP
Joined: 28 Dec 2005
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Re: nice algebra [#permalink]  12 Jan 2008, 05:09
Im getting B, 6 boxes

Initially we have a total weight of 540 lbs (30*18). We want to reduce to a total weight of 420 lbs (14*80). The difference is 120 lbs. Since we are told the number of 10 lb boxes isnt going to change, this difference must be due to the number of 20 lb boxes.

120 lbs / 20 lb/box = 6 boxes
Manager
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Re: nice algebra [#permalink]  12 Jan 2008, 05:16
Quote:
We want to reduce to a total weight of 420 lbs (14*80).

sorry, how did you get 80? thank you
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Re: nice algebra [#permalink]  12 Jan 2008, 05:20
CaspAreaGuy wrote:
Quote:
We want to reduce to a total weight of 420 lbs (14*80).

sorry, how did you get 80? thank you

Sorry, that was a typo. Should be 14*30
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Re: nice algebra [#permalink]  12 Jan 2008, 05:20
marcodonzelli wrote:
pmenon wrote:
Im getting B, 6 boxes

Initially we have a total weight of 540 lbs (30*18). We want to reduce to a total weight of 420 lbs (14*80). The difference is 120 lbs. Since we are told the number of 10 lb boxes isnt going to change, this difference must be due to the number of 20 lb boxes.

120 lbs / 20 lb/box = 6 boxes

OA is D

OK, I think I know where I went wrong. Ill be back !
Manager
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Re: nice algebra [#permalink]  12 Jan 2008, 05:25
you said the number of 10pound boxes is constant and that was usefull comment cause initially i was trying to figure out how many 20p boxes you need to take out provided you keep the number of all boxes constant
Director
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Re: nice algebra [#permalink]  12 Jan 2008, 14:43
marcodonzelli 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

D.

let x be the number of 10 pound boxes.
therefore [10x + 20(30-x)]/30 = 18

solving this you get x = 6

now setup the equation if y boxes were removed from the 24 (30-x = 30-6 = 24) twenty pound boxes

so you get [60 + 20(24 - y)] /(30- y) = 14

solving for this you get y = 20 boxes for removal.
Re: nice algebra   [#permalink] 12 Jan 2008, 14:43
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