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# There are 30 boxes with average weight 18. The box weighs

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There are 30 boxes with average weight 18. The box weighs [#permalink]

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30 Apr 2004, 10:10
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There are 30 boxes with average weight 18. The box weighs either 20 lb or 10 lb. How many 20 lb boxes are to be removed to get an average weight of 14 lb?
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30 Apr 2004, 11:32
m = no of 20 lb boxes
n = no of 10 lb boxes

( 20m+10n ) / 30 = 18
20m + 10n = 18 * 30
also m+n = 30
So n = 6 and m = 24

No we want

(x*20 + 6 * 10 ) / ( x+6 ) = 14
20x + 6*10 = 14x + 14*6
6x = 14*6 - 10*6 = 4 * 6
x = 4

x = 4 = no of 20 lb boxes.

Earlier we had 24 boxed now we have 4 boxes.
so 20 boxes should be removed.
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11 May 2004, 00:06
hallelujah1234 wrote:
There are 30 boxes with average weight 18. The box weighs either 20 lb or 10 lb. How many 20 lb boxes are to be removed to get an average weight of 14 lb?

24 20lbs-boxes, and 6 10-lbs boxes.

14: 4 20-lbs boxes and 6 10-lbs boxes.

20 boxes.
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12 May 2004, 13:52
but I am just trying to put it so that it could be solve few seconds faster

Let Z be total weight initial
so first equation is
z/30 = 18
z = 540

second equation is
(540-20x)/(30-x) = 14
x = 20
_________________

lets do it together....

12 May 2004, 13:52
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