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?
Let x be the number of smaller boxes,
y be the number of bigger boxes.
x + y = 30 -> (1)
(10X+20Y)/(X+Y) = 18 -> (2)
Solving equn 1 and 2 gives x = 6, and y = 24.
Let 'z' be the number after some number of bigger boxes are removed.
Then (10x + 20z)/(x+z) = 14, we found that x = 6, substituting we get
z = 4,
Number of boxes to be removed, Y - Z = 24 - 4 hence 20 boxes to be removed.