NandishSS wrote:Each of the 15 boxes in a certain warehouse is either 5 pounds or 10 pounds, and the average (arithmetic mean) weight of the boxes in the warehouse is 8 pounds. If the average weight of the boxes in the warehouse is 8 pounds also by removing 5 boxes, how many 10-pound boxes must be removed?
(A) 1 (B) 2 (C) 3 (D) 4 (E) 5
Each of the 15 boxes in a certain warehouse is either 5 pounds or 10 pounds, and the average (arithmetic mean) weight of the boxes in the warehouse is 8 pounds.
15 boxes have an average weight of 8 pounds.
So, the TOTAL weight = (15)(8) =
120 pounds.
IMPORTANT: If there were an EQUAL number of 5-pound boxes and 10-pound boxes, the average weight WOULD BE 7.5 pounds (i.e., the average of 5 pounds and 10 pounds). HOWEVER, the average weight is 8 pounds, which is closer to 10 pounds than it is to 5 pounds. This tells us
there are more 10-pound boxes than 5-pound boxes.
So, let's TEST some possible scenarios:
8 10-pound boxes and 7 5-pound boxes
Does this yield a TOTAL weight of
120 pounds?
(8)(10) + (7)(5) = 80 + 35 =
115 . . . CLOSE BUT NOT QUITE
9 10-pound boxes and 6 5-pound boxes
Does this yield a TOTAL weight of
120 pounds?
(9)(10) + (6)(5) = 90 + 20 =
120 PERFECT!!
So, we start with
9 10-pound boxes and 6 5-pound boxes
IMPORTANT ASIDE: the ratio of 10-pound boxes to 5-pound boxes = 9 : 6 =
3 : 2
The average weight of the boxes in the warehouse is 8 pounds also by removing 5 boxes, how many 10-pound boxes must be removed?
NOTICE that the average weight of the boxes is 8 pounds BEFORE removing the five boxes, and the average weight is ALSO 8 pounds AFTER removing the 5 boxes. So, it must be the case that the five boxes we removed must also have an average weight of 8 pounds.
Well, we already learned that when the ratio of 10-pound boxes to 5-pound boxes is
3 : 2, the average weight is 8 pounds.
So, among the five boxes we remove,
3 must be 10-pound boxes, and
2 must be 5-pound boxes
Answer:
C
