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Boxes: Averages Problem

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by tonebeeze » Tue Apr 26, 2011 3:20 pm
Each of the 30 boxes in a certain shipment weighs either 10 or 20 pounds, and the average 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?
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by Tani » Tue Apr 26, 2011 3:42 pm
Assume you have x 10# boxes and y 20# boxes.

x+y = 30
and 10x +20Y = 18*30 = 540

This tells us we have 24 20# boxes and 6 10# boxes.

The easy way to do this at this point would be to backsolve, but since you haven't given me tha answer choices we'll have to do a little math.

we still have 6 10# boxes, but need a new number (z)of 20# boxes, we set it up as follows:

6*10 + 20*Z = 14 (6+Z) That gives us 4 20# boxes remaining. We had to get rid of 20 20# boxes.

Looking at it logically, Since the average is now less than the average of 20# and 10#, there will need to be more 10# boxes than 20# boxes in the shipment.
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by Anurag@Gurome » Tue Apr 26, 2011 8:24 pm
tonebeeze wrote:Each of the 30 boxes in a certain shipment weighs either 10 or 20 pounds, and the average 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?
Before removal:
  • Say, number of 10 pound boxes is n.
    Hence, number of 20 pound boxes is (30 - n)

    Therefore, [10n + 20*(30 - n)] = 18*30 ........................... (A)
After removal:
  • Number of 10 pound boxes is n
    Say, number of 20 pound boxes removed is m
    Hence, number of 20 pound boxes is (30 - n - m)

    Therefore, [10n + 20*(30 - n - m)] = 14*(30 - m) ............ (B)
Subtracting (B) from (A)
  • 20m = 18*30 - 14*30 + 14m
    => 6m = 4*30
    => m = 4*5 = 20
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by GMATGuruNY » Wed Apr 27, 2011 1:29 am
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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by mk101 » Wed Apr 27, 2011 4:53 am
The boxes are either 20 lb or 10 lb and the average wt = 18 lb

Total wt - wt of the boxes removed = wt of the remaining boxes

18 *30 - 20*x = 14 *(30 -x)

x = 20

where x is the number of 20 lb boxes removed
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