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

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Joined: 31 Dec 1969
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Each of the 30 boxes in a certain shipment with either 10 [#permalink]

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20 Oct 2004, 08:53
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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20 Oct 2004, 11:54
D. 20
(Calculations take some time... maybe there is a faster way..)

First, we know the average and that there are 30 boxes.
10A + 20(30-A) = 30*18.
We get A=6 which means there are 24 boxes of 20 pounds.

Now we only remove some of the 20-pound boxes. Let's say we remove X boxes.

6*10 + (24-X)*20 = (30-X)*14.

Solve and get X=20.
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20 Oct 2004, 13:27
D) 20
Let x = # of 10lbs boxes
10x + 20(30-x) = 18*30
x = 6
Let y = # of 20lbs boxes to be removed
10*6 + 20(24-y) = 14(30-y)
y=20
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Paul

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20 Oct 2004, 16:01
Also got D, same approach
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21 Oct 2004, 12:50
Got 20 as well by the same method.
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