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
We can plug in the answers, which represent the number of 20-pound boxes that should be removed.
Total current weight = 30*18=540.
Answer choice C: 10 of the 20-pound boxes removed.
New total weight = 540 - 10*20 = 340.
New number of boxes = 30-10 = 20.
New average = 340/20 = 17.
The resulting average needs to be smaller, so more 20-pound boxes need to be removed.
Eliminate A, B, and C.
Answer choice D: 20 of the 20-pound boxes removed.
New total weight = 540 - 20*20 = 140.
New number of boxes = 30-20 = 10.
New average = 140/10 = 14. Success!
The correct answer is
D.
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