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by beater » Tue Sep 16, 2008 1:29 pm
Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and 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: PS

by parallel_chase » Tue Sep 16, 2008 3:06 pm
beater wrote:Each of the 30 boxes in a certain shipment weighs either 10 pounds or 20 pounds, and 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 + 20 (30-x) = 18*30

10x + 600 - 20x = 540

60 = 10x

x = 6


30-x = 30-6 = 24 20lbs boxes

Let k be 20lbs boxes removed

60 + 20(24-k) = 14*(30-k)

60 + 480 - 20k = 420 - 14k

60+60 = 6k

k = 120/6 = 20

Hence D is the answer.
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by tendays2go » Wed Sep 17, 2008 3:09 am
IMO: D

when the average weight is 18, then
10 pound boxes = 6
20 pound boxes = 24 (easy to calculate)

Nox, to reduce the average weight to 14, let total boxes be Y, then:
10 pound boxes = 6
20 pound boxes = Y - 6

thus, 10*6 + 20*(Y - 6) = 14*Y i.e. 60 + 20Y -120 = 14Y
or 6Y = 60
thus,
10 pound boxes = 6
20 pound boxes = 4
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by beater » Wed Sep 17, 2008 11:40 am
Thanks for the wonderful explanation guys!
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